%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 06:56:06 AM UTC 2026
% Result : Unsatisfiable 39.91s 10.81s
% Output : Refutation 39.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 108 ( 2 ~; 0 |; 0 &; 106 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(weak_fixed_point_decl,type,
weak_fixed_point: $i > $i ).
thf(fixed_pt_decl,type,
fixed_pt: $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(s_decl,type,
s: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(i_decl,type,
i: $i ).
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(10,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(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c @ apply ) @ apply ) @ apply ) )
= ( B @ ( C @ ( A @ apply ) @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c @ apply ) @ apply ) @ apply ) )
= ( B @ ( C @ ( A @ apply ) @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( A @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( A @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( fixed_pt @ weak_fixed_point )
!= ( fixed_pt @ weak_fixed_point @ ( fixed_pt @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
thf(7,plain,
( ( fixed_pt @ weak_fixed_point )
!= ( fixed_pt @ weak_fixed_point @ ( fixed_pt @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ weak_fixed_point )
= ( i @ ( A @ ( b @ apply ) @ ( s @ apply ) @ apply ) @ ( i @ ( A @ ( b @ apply ) @ ( s @ apply ) @ apply ) @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
thf(18,plain,
! [A: $i] :
( ( A @ weak_fixed_point )
= ( i @ ( A @ ( b @ apply ) @ ( s @ apply ) @ apply ) @ ( i @ ( A @ ( b @ apply ) @ ( s @ apply ) @ apply ) @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( i @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( i @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9196,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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
% 0.23/0.48 % Computer : n018.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 23:04:52 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.07/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.33 % [INFO] Parsing done (180ms).
% 1.54/1.34 % [INFO] Running in sequential loop mode.
% 2.18/1.76 % [INFO] eprover registered as external prover.
% 2.18/1.77 % [INFO] Scanning for conjecture ...
% 2.42/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.42/1.89 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.61/1.90 % [INFO] Problem is propositional (TPTP CNF).
% 2.61/1.91 % [INFO] Type checking passed.
% 2.61/1.91 % [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 ...
% 39.91/10.80 % External prover 'e' found a proof!
% 39.91/10.80 % [INFO] Killing All external provers ...
% 39.91/10.81 % Time passed: 10110ms (effective reasoning time: 9457ms)
% 39.91/10.81 % Axioms used in derivation (5): weak_fixed_point, c_definition, s_definition, b_definition, i_definition
% 39.91/10.81 % No. of inferences in proof: 13
% 39.91/10.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10110 ms resp. 9457 ms w/o parsing
% 39.91/10.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.91/10.86 % [INFO] Killing All external provers ...
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