%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 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 06:56:24 AM UTC 2026
% Result : Unsatisfiable 2.94s 1.83s
% Output : Refutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 148 ( 4 ~; 4 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(k_decl,type,
k: $i ).
thf(abstraction_decl,type,
abstraction: $i ).
thf(projection1_decl,type,
projection1: $i ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(projection2_decl,type,
projection2: $i ).
thf(eq_decl,type,
eq: $i ).
thf(n_decl,type,
n: $i > $i > $i ).
thf(k_projection1_decl,type,
k_projection1: $i ).
thf(k_projection2_decl,type,
k_projection2: $i ).
thf(s_decl,type,
s: $i ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection2 @ apply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection2 @ apply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ pair ) @ ( eq @ apply ) )
= projection2 )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ pair ) @ ( eq @ apply ) )
= projection2 )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
( s
= ( projection2 @ ( k @ apply ) @ ( s @ ( k @ apply ) @ pair ) @ ( eq @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_referential) ).
thf(41,plain,
( s
= ( projection2 @ ( k @ apply ) @ ( s @ ( k @ apply ) @ pair ) @ ( eq @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
thf(34,plain,
projection1 != projection2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( projection2 @ apply ) @ ( A @ ( projection1 @ apply ) @ pair ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( projection2 @ apply ) @ ( A @ ( projection1 @ apply ) @ pair ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
( ( projection2 @ ( k @ apply ) )
= k_projection2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection2) ).
thf(39,plain,
( ( projection2 @ ( k @ apply ) )
= k_projection2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection1 @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection1 @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ n ) @ ( A @ apply ) )
!= ( B @ ( A @ n ) @ ( B @ apply ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ n ) @ ( A @ apply ) )
!= ( B @ ( A @ n ) @ ( B @ apply ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( A @ pair ) @ ( eq @ apply ) )
= projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ pair ) @ ( eq @ apply ) )
= projection1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( abstraction @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( k @ apply ) @ ( A @ apply ) @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( abstraction @ apply ) @ apply ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( k @ apply ) @ ( A @ apply ) @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ pair ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( A @ apply ) @ pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ pair ) @ apply ) )
= ( C @ ( B @ apply ) @ ( C @ ( A @ apply ) @ pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( ( projection1 @ ( k @ apply ) )
= k_projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection1) ).
thf(37,plain,
( ( projection1 @ ( k @ apply ) )
= k_projection1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(66,plain,
$false,
inference(e,[status(thm)],[14,20,28,41,34,22,39,18,31,26,15,24,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % 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
% 0.11/0.50 % Computer : n018.cluster.edu
% 0.11/0.50 % Model : x86_64 x86_64
% 0.11/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.50 % Memory : 8046.5625MB
% 0.11/0.50 % OS : Linux 6.8.0-71-generic
% 0.11/0.50 % CPULimit : 300
% 0.11/0.50 % WCLimit : 300
% 0.11/0.50 % DateTime : Sat Sep 26 23:13:53 UTC 2026
% 0.11/0.50 % CPUTime :
% 0.11/0.50 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
% 0.91/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.23 % [INFO] Parsing done (133ms).
% 1.23/1.23 % [INFO] Running in sequential loop mode.
% 1.68/1.42 % [INFO] eprover registered as external prover.
% 1.68/1.42 % [INFO] Scanning for conjecture ...
% 1.68/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.68/1.49 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.68/1.49 % [INFO] Problem is propositional (TPTP CNF).
% 1.68/1.50 % [INFO] Type checking passed.
% 1.92/1.50 % [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 ...
% 2.94/1.83 % External prover 'e' found a proof!
% 2.94/1.83 % [INFO] Killing All external provers ...
% 2.94/1.83 % Time passed: 1186ms (effective reasoning time: 591ms)
% 2.94/1.83 % Axioms used in derivation (11): pairwise_application, k_projection1, extensionality2, k_projection2, projection1, projection2, pairing, equality, extensionality1, self_referential, different_projections
% 2.94/1.83 % No. of inferences in proof: 27
% 2.94/1.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1186 ms resp. 591 ms w/o parsing
% 2.94/1.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.94/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------