%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL075-1 : 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 : n016.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 4.98s 22.30s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 146 ( 6 ~; 4 |; 0 &; 136 @)
% ( 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 : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(b_decl,type,
b: $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(k_decl,type,
k: $i ).
thf(projection1_decl,type,
projection1: $i ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(projection2_decl,type,
projection2: $i ).
thf(abstraction_decl,type,
abstraction: $i ).
thf(eq_decl,type,
eq: $i ).
thf(n_decl,type,
n: $i > $i > $i ).
thf(7,axiom,
! [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(25,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)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ pair ) @ ( eq @ apply ) )
= projection2 )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ pair ) @ ( eq @ apply ) )
= projection2 )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( projection2 @ apply ) @ ( A @ ( projection1 @ apply ) @ pair ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( projection2 @ apply ) @ ( A @ ( projection1 @ apply ) @ pair ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ pair ) @ ( eq @ apply ) )
= projection1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ pair ) @ ( eq @ apply ) )
= projection1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ c @ ( A @ b @ ( A @ apply ) @ apply ) )
!= ( A @ b @ ( A @ b @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
thf(12,plain,
! [A: $i] :
( ( A @ c @ ( A @ b @ ( A @ apply ) @ apply ) )
!= ( A @ b @ ( A @ b @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
thf(35,plain,
projection1 != projection2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(23,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(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection2 @ apply ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection2 @ apply ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( k @ apply ) @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,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(32,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)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection1 @ apply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ pair ) @ ( projection1 @ apply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(287,plain,
$false,
inference(e,[status(thm)],[25,29,21,27,12,35,23,19,15,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.05/20.37 % CPULimit : 300
% 0.05/20.37 % WCLimit : 300
% 0.05/20.37 % DateTime : Sat Sep 26 23:11:40 UTC 2026
% 0.05/20.37 % CPUTime :
% 0.05/20.37 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
% 0.29/20.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.29/21.00 % [INFO] Parsing done (145ms).
% 0.29/21.01 % [INFO] Running in sequential loop mode.
% 1.60/21.28 % [INFO] eprover registered as external prover.
% 1.60/21.28 % [INFO] Scanning for conjecture ...
% 1.81/21.34 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.81/21.37 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.81/21.38 % [INFO] Problem is propositional (TPTP CNF).
% 1.81/21.38 % [INFO] Type checking passed.
% 1.81/21.38 % [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 ...
% 4.98/22.30 % External prover 'e' found a proof!
% 4.98/22.30 % [INFO] Killing All external provers ...
% 4.98/22.30 % Time passed: 1807ms (effective reasoning time: 1283ms)
% 4.98/22.30 % Axioms used in derivation (10): abstraction, k_definition, pairwise_application, extensionality2, projection1, projection2, different_projections, pairing, equality, extensionality1
% 4.98/22.30 % No. of inferences in proof: 23
% 4.98/22.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1807 ms resp. 1283 ms w/o parsing
% 4.98/22.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.98/22.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------