%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Wed Oct 7 10:11:08 AM UTC 2026
% Result : Unsatisfiable 38.75s 6.79s
% Output : CNFRefutation 38.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 67 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 216 ( 13 ~; 8 |; 0 &; 195 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_abstraction,type,
abstraction: $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_k,type,
k: $i > $i ).
thf(tp_n,type,
n: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( apply @ identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( apply @ ( k @ X ) @ Y )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
( ( k @ ( k @ b ) )
!= ( apply @ abstraction @ ( k @ ( k @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( apply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( k @ X ) @ Y )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( k @ ( k @ b ) )
!= ( apply @ abstraction @ ( k @ ( k @ b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [X: $i,Y: $i] :
( ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,plain,
( ( ( k @ ( k @ b ) )
!= ( apply @ abstraction @ ( k @ ( k @ b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(17,plain,
( ( ( k @ ( k @ b ) )
!= ( apply @ abstraction @ ( k @ ( k @ b ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ ( k @ X ) @ Y )
= X ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( ( apply @ X @ ( n @ X @ Y ) )
!= ( apply @ Y @ ( n @ X @ Y ) ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( apply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
( ( ( k @ ( k @ b ) )
= ( apply @ abstraction @ ( k @ ( k @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
( ( apply @ ( k @ SV1 ) @ SY8 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV2: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SY9 ) @ SY10 )
= ( apply @ ( apply @ SV2 @ ( k @ SY10 ) ) @ ( apply @ SY9 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV3: $i] :
( ( ! [SY11: $i] :
( ( ( apply @ SV3 @ ( n @ SV3 @ SY11 ) )
!= ( apply @ SY11 @ ( n @ SV3 @ SY11 ) ) )
| ( SV3 = SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV4: $i] :
( ( ( apply @ identity @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV5: $i,SV1: $i] :
( ( ( apply @ ( k @ SV1 ) @ SV5 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY12: $i] :
( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SV6 ) @ SY12 )
= ( apply @ ( apply @ SV2 @ ( k @ SY12 ) ) @ ( apply @ SV6 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( apply @ SV3 @ ( n @ SV3 @ SV7 ) )
!= ( apply @ SV7 @ ( n @ SV3 @ SV7 ) ) )
| ( SV3 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV8: $i,SV6: $i,SV2: $i] :
( ( ( apply @ ( apply @ ( apply @ abstraction @ SV2 ) @ SV6 ) @ SV8 )
= ( apply @ ( apply @ SV2 @ ( k @ SV8 ) ) @ ( apply @ SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( apply @ SV3 @ ( n @ SV3 @ SV7 ) )
!= ( apply @ SV7 @ ( n @ SV3 @ SV7 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV7: $i,SV3: $i] :
( ( ( ( apply @ SV3 @ ( n @ SV3 @ SV7 ) )
= ( apply @ SV7 @ ( n @ SV3 @ SV7 ) ) )
= $false )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,34,32,29,28,27]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n005.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 18:34:14 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.75/6.79
% 38.75/6.79 No.of.Axioms: 5
% 38.75/6.79
% 38.75/6.79 Length.of.Defs: 0
% 38.75/6.79
% 38.75/6.79 Contains.Choice.Funs: false
% 38.75/6.79
% 38.75/6.79 ********************************
% 38.75/6.79 * All subproblems solved! *
% 38.75/6.79 ********************************
% 38.75/6.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 38.75/6.79
% 38.75/6.79 %**** Beginning of derivation protocol ****
% 38.75/6.79 % SZS output start CNFRefutation
% See solution above
% 38.75/6.79
% 38.75/6.79 %**** End of derivation protocol ****
% 38.75/6.79 %**** no. of clauses in derivation: 36 ****
% 38.75/6.79 %**** clause counter: 35 ****
% 38.75/6.79
% 38.75/6.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------