%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 10:10:52 AM UTC 2026
% Result : Unsatisfiable 8.48s 1.64s
% Output : CNFRefutation 8.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 101 ( 62 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 286 ( 6 ~; 0 |; 0 &; 280 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_fixed_pt,type,
fixed_pt: $i ).
thf(tp_i,type,
i: $i ).
thf(tp_s,type,
s: $i ).
thf(tp_weak_fixed_point,type,
weak_fixed_point: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( weak_fixed_point @ X )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
thf(2,axiom,
! [X: $i] :
( ( apply @ i @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ c @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_definition) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ s @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( weak_fixed_point @ X )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i] :
( ( apply @ i @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ c @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ s @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(18,plain,
( ( ( weak_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ s @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ b @ X ) @ Y ) @ Z )
= ( apply @ X @ ( apply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apply @ ( apply @ ( apply @ c @ X ) @ Y ) @ Z )
= ( apply @ ( apply @ X @ Z ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( apply @ i @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( weak_fixed_point @ X )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ( weak_fixed_point @ fixed_pt )
= ( apply @ fixed_pt @ ( weak_fixed_point @ fixed_pt ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ( apply @ ( apply @ ( apply @ s @ SV1 ) @ SY11 ) @ SY12 )
= ( apply @ ( apply @ SV1 @ SY12 ) @ ( apply @ SY11 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV2 ) @ SY13 ) @ SY14 )
= ( apply @ SV2 @ ( apply @ SY13 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ( apply @ ( apply @ ( apply @ c @ SV3 ) @ SY15 ) @ SY16 )
= ( apply @ ( apply @ SV3 @ SY16 ) @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ( apply @ i @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV5: $i] :
( ( ( weak_fixed_point @ SV5 )
= ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ SV5 ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ SV5 ) ) @ i ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY17: $i] :
( ( apply @ ( apply @ ( apply @ s @ SV1 ) @ SV6 ) @ SY17 )
= ( apply @ ( apply @ SV1 @ SY17 ) @ ( apply @ SV6 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY18: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV2 ) @ SV7 ) @ SY18 )
= ( apply @ SV2 @ ( apply @ SV7 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ( apply @ ( apply @ ( apply @ c @ SV3 ) @ SV8 ) @ SY19 )
= ( apply @ ( apply @ SV3 @ SY19 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV9: $i,SV6: $i,SV1: $i] :
( ( ( apply @ ( apply @ ( apply @ s @ SV1 ) @ SV6 ) @ SV9 )
= ( apply @ ( apply @ SV1 @ SV9 ) @ ( apply @ SV6 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV10: $i,SV7: $i,SV2: $i] :
( ( ( apply @ ( apply @ ( apply @ b @ SV2 ) @ SV7 ) @ SV10 )
= ( apply @ SV2 @ ( apply @ SV7 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV11: $i,SV8: $i,SV3: $i] :
( ( ( apply @ ( apply @ ( apply @ c @ SV3 ) @ SV8 ) @ SV11 )
= ( apply @ ( apply @ SV3 @ SV11 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,37,36,35,31,30,29]) ).
thf(39,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n009.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 18:31:17 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.48/1.64
% 8.48/1.64 No.of.Axioms: 6
% 8.48/1.64
% 8.48/1.64 Length.of.Defs: 0
% 8.48/1.64
% 8.48/1.64 Contains.Choice.Funs: false
% 8.48/1.64 .
% 8.48/1.64
% 8.48/1.64 ********************************
% 8.48/1.64 * All subproblems solved! *
% 8.48/1.64 ********************************
% 8.48/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.48/1.64
% 8.48/1.64 %**** Beginning of derivation protocol ****
% 8.48/1.64 % SZS output start CNFRefutation
% See solution above
% 8.48/1.64
% 8.48/1.64 %**** End of derivation protocol ****
% 8.48/1.64 %**** no. of clauses in derivation: 39 ****
% 8.48/1.64 %**** clause counter: 38 ****
% 8.48/1.64
% 8.48/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------