%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL006-2 : 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 : n026.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 06:56:09 AM UTC 2026
% Result : Unsatisfiable 20.84s 5.37s
% Output : Refutation 20.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 126 ( 4 ~; 2 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(fixed_point_decl,type,
fixed_point: $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(s_decl,type,
s: $i ).
thf(k_decl,type,
k: $i ).
thf(fixed_pt_decl,type,
fixed_pt: $i ).
thf(1,negated_conjecture,
~ ( k @ ( s @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( s @ apply ) @ ( s @ ( s @ apply ) @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ fixed_point ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
thf(5,plain,
~ ( k @ ( s @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( s @ apply ) @ ( s @ ( s @ apply ) @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ fixed_point ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( s @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( A @ apply ) @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( s @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( A @ apply ) @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ fixed_point )
| ( ( fixed_pt @ ( A @ apply ) )
!= ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
thf(11,plain,
! [A: $i] :
( ( A @ fixed_point )
| ( ( fixed_pt @ ( A @ apply ) )
!= ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2208,plain,
$false,
inference(e,[status(thm)],[5,7,9,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.22/0.50 % Computer : n026.cluster.edu
% 0.22/0.50 % Model : x86_64 x86_64
% 0.22/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.50 % Memory : 8046.5625MB
% 0.22/0.50 % OS : Linux 6.8.0-71-generic
% 0.22/0.50 % CPULimit : 300
% 0.22/0.50 % WCLimit : 300
% 0.22/0.50 % DateTime : Sat Sep 26 23:07:26 UTC 2026
% 0.22/0.51 % CPUTime :
% 0.22/0.51 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
% 0.96/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.14 % [INFO] Parsing done (148ms).
% 1.30/1.15 % [INFO] Running in sequential loop mode.
% 1.91/1.48 % [INFO] eprover registered as external prover.
% 1.91/1.49 % [INFO] Scanning for conjecture ...
% 2.17/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.17/1.59 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.17/1.59 % [INFO] Problem is propositional (TPTP CNF).
% 2.41/1.60 % [INFO] Type checking passed.
% 2.41/1.60 % [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 ...
% 20.84/5.36 % External prover 'e' found a proof!
% 20.84/5.37 % [INFO] Killing All external provers ...
% 20.84/5.37 % Time passed: 4718ms (effective reasoning time: 4210ms)
% 20.84/5.37 % Axioms used in derivation (3): s_definition, k_definition, strong_fixed_point
% 20.84/5.37 % No. of inferences in proof: 9
% 20.84/5.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4718 ms resp. 4210 ms w/o parsing
% 20.84/5.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.84/5.39 % [INFO] Killing All external provers ...
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