%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL004-3 : 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 : n013.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 3.16s 7.97s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 102 ( 2 ~; 0 |; 0 &; 100 @)
% ( 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 : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(s_decl,type,
s: $i ).
thf(k_decl,type,
k: $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(1,negated_conjecture,
( ( y @ ( x @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ apply ) @ apply ) )
!= ( y @ ( x @ ( x @ apply ) @ apply ) @ ( y @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_combinator) ).
thf(4,plain,
( ( y @ ( x @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ apply ) @ ( k @ ( k @ ( s @ apply ) @ apply ) @ ( s @ apply ) @ ( k @ apply ) @ ( s @ apply ) @ apply ) @ apply ) @ apply ) )
!= ( y @ ( x @ ( x @ apply ) @ apply ) @ ( y @ apply ) ) ),
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(14,plain,
$false,
inference(e,[status(thm)],[4,7,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % 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
% 0.13/5.47 % Computer : n013.cluster.edu
% 0.13/5.47 % Model : x86_64 x86_64
% 0.13/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.47 % Memory : 8046.5625MB
% 0.13/5.47 % OS : Linux 6.8.0-71-generic
% 0.13/5.47 % CPULimit : 300
% 0.13/5.47 % WCLimit : 300
% 0.13/5.47 % DateTime : Sat Sep 26 23:04:11 UTC 2026
% 0.13/5.47 % CPUTime :
% 0.13/5.47 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
% 0.83/6.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/6.45 % [INFO] Parsing done (243ms).
% 0.95/6.47 % [INFO] Running in sequential loop mode.
% 1.63/6.97 % [INFO] eprover registered as external prover.
% 1.63/6.98 % [INFO] Scanning for conjecture ...
% 1.87/7.10 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.99/7.15 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.99/7.16 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/7.17 % [INFO] Type checking passed.
% 1.99/7.18 % [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 ...
% 3.16/7.96 % External prover 'e' found a proof!
% 3.16/7.96 % [INFO] Killing All external provers ...
% 3.16/7.96 % Time passed: 2279ms (effective reasoning time: 1482ms)
% 3.16/7.97 % Axioms used in derivation (2): s_definition, k_definition
% 3.16/7.97 % No. of inferences in proof: 7
% 3.16/7.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2279 ms resp. 1482 ms w/o parsing
% 3.16/8.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/8.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------