%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL044-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : 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 06:56:16 AM UTC 2026
% Result : Unsatisfiable 38.27s 13.07s
% Output : Refutation 38.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 57 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 714 ( 39 ~; 23 |; 0 &; 652 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(fixed_point_decl,type,
fixed_point: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(n_decl,type,
n: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(fixed_pt_decl,type,
fixed_pt: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[9]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( n @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ ( C @ ( A @ apply ) @ apply ) @ apply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( n @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ ( C @ ( A @ apply ) @ apply ) @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( n @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ ( C @ ( A @ apply ) @ apply ) @ apply ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(1,negated_conjecture,
( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
thf(6,plain,
( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [A: $i] :
( ( true @ ( A @ fixed_point @ ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) @ ( fixed_pt @ ( A @ apply ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
thf(15,plain,
! [A: $i] :
( ( true @ ( A @ fixed_point @ ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) @ ( fixed_pt @ ( A @ apply ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [A: $i] :
( ( true @ ( A @ fixed_point @ ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) @ ( fixed_pt @ ( A @ apply ) @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( A @ fixed_point @ ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) @ ( fixed_pt @ ( A @ apply ) @ ifeq ) ) ) )
!= ( D @ ( C @ ( B @ ( B @ ifeq ) ) ) ) )
| ( true = C ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true != D )
| ( ( A @ fixed_point )
!= C )
| ( ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) )
!= B )
| ( ( fixed_pt @ ( A @ apply ) )
!= B )
| ( true = C ) ),
inference(simp,[status(thm)],[17]) ).
thf(21,plain,
! [A: $i] :
( ( ( fixed_pt @ ( A @ apply ) @ ( fixed_pt @ apply ) )
!= ( fixed_pt @ ( A @ apply ) ) )
| ( ( A @ fixed_point )
= true ) ),
inference(simp,[status(thm)],[19]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( A @ apply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
thf(11,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(12,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( A @ apply ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(262,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
!= ( F @ ( E @ ( F @ ( D @ apply ) @ apply ) @ apply ) ) )
| ( ( C @ ( B @ apply ) @ ( A @ apply ) )
= ( F @ ( E @ ( D @ ( n @ apply ) @ apply ) @ apply ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apply ) @ ( B @ apply ) )
= ( B @ ( A @ ( b @ ( n @ apply ) @ apply ) @ apply ) ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( b )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apply ) @ ( B @ apply ) )
= ( B @ ( A @ ( b @ ( n @ apply ) @ apply ) @ apply ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(7,plain,
( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ),
inference(lifteq,[status(thm)],[7]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
!= ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) ) )
| ( ( b @ ( b @ ( C @ ( B @ apply ) @ ( A @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C != n )
| ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) ) )
| ( ( b @ ( b @ ( C @ ( B @ apply ) @ ( A @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[38]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) ) )
| ( ( b @ ( b @ ( n @ ( B @ apply ) @ ( A @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[52]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
!= ( b @ ( b @ apply ) ) )
| ( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( C @ ( B @ apply ) @ ( A @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C != b )
| ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= b )
| ( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( C @ ( B @ apply ) @ ( A @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[46]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= b )
| ( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( B @ apply ) @ ( A @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[51]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( b @ apply ) @ apply ) @ apply ) )
!= ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) @ apply ) ) )
| ( ( C @ ( B @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C != b )
| ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) ) )
| ( ( C @ ( B @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[42]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( b @ apply ) @ apply ) )
!= ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ ( b @ apply ) ) )
| ( ( b @ ( B @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B
!= ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) ) )
| ( ( A @ ( b @ apply ) )
!= b )
| ( ( b @ ( B @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[62]) ).
thf(134,plain,
! [A: $i] :
( ( ( A @ ( b @ apply ) )
!= b )
| ( ( b @ ( b @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ apply ) @ apply ) @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(simp,[status(thm)],[74]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ ( b @ apply ) )
!= b )
| ( ( b @ ( b @ apply ) @ ( n @ ( n @ ( b @ ( b @ apply ) @ ( n @ apply ) @ ( n @ apply ) @ apply ) @ ( b @ ( b @ apply ) @ apply ) @ ( n @ apply ) @ apply ) @ apply ) @ ( A @ apply ) @ fixed_point )
!= true ) ),
inference(rewrite,[status(thm)],[134,12]) ).
thf(2197,plain,
$false,
inference(e,[status(thm)],[10,14,6,21,9,471,64,12,63,16,11,8,173,13,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL044-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.12 % 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
% 0.22/0.49 % Computer : n026.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 23:10:42 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.44/1.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.57 % [INFO] Parsing done (249ms).
% 1.80/1.59 % [INFO] Running in sequential loop mode.
% 2.78/2.18 % [INFO] eprover registered as external prover.
% 2.78/2.19 % [INFO] Scanning for conjecture ...
% 3.08/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.08/2.37 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.08/2.38 % [INFO] Problem is propositional (TPTP CNF).
% 3.08/2.39 % [INFO] Type checking passed.
% 3.25/2.40 % [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 ...
% 38.27/13.06 % External prover 'e' found a proof!
% 38.27/13.07 % [INFO] Killing All external provers ...
% 38.27/13.07 % Time passed: 12369ms (effective reasoning time: 11468ms)
% 38.27/13.07 % Axioms used in derivation (4): ifeq_axiom, n_definition, strong_fixed_point, b_definition
% 38.27/13.07 % No. of inferences in proof: 35
% 38.27/13.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12369 ms resp. 11468 ms w/o parsing
% 38.27/13.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.27/13.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------