%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 07:52:26 AM UTC 2026
% Result : Theorem 5.48s 2.88s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 255 ( 0 equ; 0 cnn)
% Maximal formula atoms : 84 ( 42 avg)
% Number of connectives : 901 ( 255 ~; 189 |; 60 &; 397 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 25 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 146 ( 0 ^; 143 !; 3 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p12_decl,type,
p12: $i > $o ).
thf(p10_decl,type,
p10: $i > $o ).
thf(p8_decl,type,
p8: $i > $o ).
thf(p6_decl,type,
p6: $i > $o ).
thf(p4_decl,type,
p4: $i > $o ).
thf(p2_decl,type,
p2: $i > $o ).
thf(p7_decl,type,
p7: $i > $o ).
thf(p5_decl,type,
p5: $i > $o ).
thf(p1_decl,type,
p1: $i > $o ).
thf(p3_decl,type,
p3: $i > $o ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ( G @ p1 )
& ( G @ p2 )
& ( G @ p3 )
& ( G @ p4 )
& ( G @ p5 )
& ( G @ p6 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ( ~ ! [E: $i] :
( ~ ( ~ ! [F: $i] :
( ~ ~ ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p1 )
& ( I @ p2 ) )
| ( ~ ( I @ p2 )
& ~ ( I @ p1 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p2 )
& ( I @ p3 ) )
| ( ~ ( I @ p3 )
& ~ ( I @ p2 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ( E @ p4 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p3 )
& ( I @ p4 ) )
| ( ~ ( I @ p4 )
& ~ ( I @ p3 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p4 )
& ( I @ p5 ) )
| ( ~ ( I @ p5 )
& ~ ( I @ p4 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p5 )
& ( I @ p1 ) )
| ( ~ ( I @ p1 )
& ~ ( I @ p5 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p7 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ~ ( G @ p2 )
& ~ ( G @ p4 )
& ~ ( G @ p6 )
& ~ ( G @ p8 )
& ~ ( G @ p10 )
& ~ ( G @ p12 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ( G @ p1 )
& ( G @ p2 )
& ( G @ p3 )
& ( G @ p4 )
& ( G @ p5 )
& ( G @ p6 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ( ~ ! [E: $i] :
( ~ ( ~ ! [F: $i] :
( ~ ~ ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p1 )
& ( I @ p2 ) )
| ( ~ ( I @ p2 )
& ~ ( I @ p1 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p2 )
& ( I @ p3 ) )
| ( ~ ( I @ p3 )
& ~ ( I @ p2 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ( E @ p4 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p3 )
& ( I @ p4 ) )
| ( ~ ( I @ p4 )
& ~ ( I @ p3 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p4 )
& ( I @ p5 ) )
| ( ~ ( I @ p5 )
& ~ ( I @ p4 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p5 )
& ( I @ p1 ) )
| ( ~ ( I @ p1 )
& ~ ( I @ p5 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p7 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ~ ( G @ p2 )
& ~ ( G @ p4 )
& ~ ( G @ p6 )
& ~ ( G @ p8 )
& ~ ( G @ p10 )
& ~ ( G @ p12 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ( G @ p1 )
& ( G @ p2 )
& ( G @ p3 )
& ( G @ p4 )
& ( G @ p5 )
& ( G @ p6 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ~ ( ~ ! [D: $i] :
( ~ ( ~ ! [E: $i] :
( ~ ( ~ ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p1 )
& ( I @ p2 ) )
| ( ~ ( I @ p2 )
& ~ ( I @ p1 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ! [F: $i] :
( ( F @ p3 )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p2 )
& ( I @ p3 ) )
| ( ~ ( I @ p3 )
& ~ ( I @ p2 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ! [E: $i] :
( ( E @ p4 )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p3 )
& ( I @ p4 ) )
| ( ~ ( I @ p4 )
& ~ ( I @ p3 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ! [D: $i] :
( ( D @ p5 )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p4 )
& ( I @ p5 ) )
| ( ~ ( I @ p5 )
& ~ ( I @ p4 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) ) )
| ~ ( C @ ( B @ r1 ) ) )
| ! [C: $i] :
( ( C @ p6 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ! [H: $i] :
( ! [I: $i] :
( ~ ( ( ( I @ p5 )
& ( I @ p1 ) )
| ( ~ ( I @ p1 )
& ~ ( I @ p5 ) ) )
| ~ ( I @ ( H @ r1 ) ) )
| ~ ( H @ ( G @ r1 ) ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ( B @ p7 )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ! [G: $i] :
( ( ~ ( G @ p2 )
& ~ ( G @ p4 )
& ~ ( G @ p6 )
& ~ ( G @ p8 )
& ~ ( G @ p10 )
& ~ ( G @ p12 ) )
| ~ ( G @ ( F @ r1 ) ) )
| ~ ( F @ ( E @ r1 ) ) )
| ~ ( E @ ( D @ r1 ) ) )
| ~ ( D @ ( C @ r1 ) ) )
| ~ ( 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/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(56,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,plain,
$false,
inference(e,[status(thm)],[4,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n011.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 23:09:43 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.20 % [INFO] Parsing done (217ms).
% 1.48/1.21 % [INFO] Running in sequential loop mode.
% 2.27/1.61 % [INFO] eprover registered as external prover.
% 2.27/1.62 % [INFO] Scanning for conjecture ...
% 2.46/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.69/1.85 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.69/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.69/1.87 % [INFO] Type checking passed.
% 2.69/1.87 % [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 ...
% 5.48/2.87 % External prover 'e' found a proof!
% 5.48/2.87 % [INFO] Killing All external provers ...
% 5.48/2.87 % Time passed: 2325ms (effective reasoning time: 1654ms)
% 5.48/2.88 % 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)>
% 5.48/2.88 % Axioms used in derivation (1): reflexivity
% 5.48/2.88 % No. of inferences in proof: 6
% 5.48/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2325 ms resp. 1654 ms w/o parsing
% 5.92/2.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.92/2.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------