%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n011.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 4.92s 1.04s
% Output : CNFRefutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 65 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 315 ( 12 ~; 7 |; 0 &; 296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 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 : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_fixed_point,type,
fixed_point: $i > $o ).
thf(tp_fixed_pt,type,
fixed_pt: $i ).
thf(tp_i,type,
i: $i ).
thf(tp_s,type,
s: $i ).
thf(1,axiom,
! [Weak_sage: $i] :
( ( Weak_sage
!= ( apply @ fixed_pt @ Weak_sage ) )
| ( fixed_point @ Weak_sage ) ),
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,
! [X: $i] :
~ ( fixed_point @ ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ),
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,
( ( ! [Weak_sage: $i] :
( ( Weak_sage
!= ( apply @ fixed_pt @ Weak_sage ) )
| ( fixed_point @ Weak_sage ) ) )
= $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,
( ( ! [X: $i] :
~ ( fixed_point @ ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( fixed_point @ ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ X ) ) @ i ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,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(19,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(20,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(21,plain,
( ( ! [X: $i] :
( ( apply @ i @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [Weak_sage: $i] :
( ( Weak_sage
!= ( apply @ fixed_pt @ Weak_sage ) )
| ( fixed_point @ Weak_sage ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( apply @ fixed_pt @ SX0 ) )
| ( fixed_point @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( fixed_point @ ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ SV1 ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ SV1 ) ) @ i ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ( apply @ ( apply @ ( apply @ s @ SV2 ) @ SY12 ) @ SY13 )
= ( apply @ ( apply @ SV2 @ SY13 ) @ ( apply @ SY12 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV3 ) @ SY14 ) @ SY15 )
= ( apply @ SV3 @ ( apply @ SY14 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( apply @ ( apply @ ( apply @ c @ SV4 ) @ SY16 ) @ SY17 )
= ( apply @ ( apply @ SV4 @ SY17 ) @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV5: $i] :
( ( ( apply @ i @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV6: $i] :
( ( ( SV6
!= ( apply @ fixed_pt @ SV6 ) )
| ( fixed_point @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV1: $i] :
( ( fixed_point @ ( apply @ ( apply @ ( apply @ s @ ( apply @ b @ SV1 ) ) @ i ) @ ( apply @ ( apply @ s @ ( apply @ b @ SV1 ) ) @ i ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY18: $i] :
( ( apply @ ( apply @ ( apply @ s @ SV2 ) @ SV7 ) @ SY18 )
= ( apply @ ( apply @ SV2 @ SY18 ) @ ( apply @ SV7 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ( apply @ ( apply @ ( apply @ b @ SV3 ) @ SV8 ) @ SY19 )
= ( apply @ SV3 @ ( apply @ SV8 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY20: $i] :
( ( apply @ ( apply @ ( apply @ c @ SV4 ) @ SV9 ) @ SY20 )
= ( apply @ ( apply @ SV4 @ SY20 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV6: $i] :
( ( ( SV6
!= ( apply @ fixed_pt @ SV6 ) )
= $true )
| ( ( fixed_point @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV10: $i,SV7: $i,SV2: $i] :
( ( ( apply @ ( apply @ ( apply @ s @ SV2 ) @ SV7 ) @ SV10 )
= ( apply @ ( apply @ SV2 @ SV10 ) @ ( apply @ SV7 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV11: $i,SV8: $i,SV3: $i] :
( ( ( apply @ ( apply @ ( apply @ b @ SV3 ) @ SV8 ) @ SV11 )
= ( apply @ SV3 @ ( apply @ SV8 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV12: $i,SV9: $i,SV4: $i] :
( ( ( apply @ ( apply @ ( apply @ c @ SV4 ) @ SV9 ) @ SV12 )
= ( apply @ ( apply @ SV4 @ SV12 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i] :
( ( ( SV6
= ( apply @ fixed_pt @ SV6 ) )
= $false )
| ( ( fixed_point @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,40,39,38,37,32,30]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-2 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.07/0.19 % Computer : n011.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 18:31:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.92/1.04
% 4.92/1.04 No.of.Axioms: 6
% 4.92/1.04
% 4.92/1.04 Length.of.Defs: 0
% 4.92/1.04
% 4.92/1.04 Contains.Choice.Funs: false
% 4.92/1.04
% 4.92/1.04 ********************************
% 4.92/1.04 * All subproblems solved! *
% 4.92/1.04 ********************************
% 4.92/1.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.92/1.04
% 4.92/1.04 %**** Beginning of derivation protocol ****
% 4.92/1.04 % SZS output start CNFRefutation
% See solution above
% 4.92/1.04
% 4.92/1.04 %**** End of derivation protocol ****
% 4.92/1.04 %**** no. of clauses in derivation: 42 ****
% 4.92/1.04 %**** clause counter: 41 ****
% 4.92/1.04
% 4.92/1.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------