%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 11:07:18 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 470 ( 55 ~; 59 |; 12 &; 340 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-3 aty)
% Number of variables : 120 ( 0 ^; 104 !; 16 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_r,type,
r: $i > $i > $i > $o ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [Y: $i,X: $i,Z: $i,Z1: $i] :
( ( r @ Y @ X @ Z )
=> ( ( r @ Z @ X @ Z1 )
=> ( r @ Y @ ( succ @ X ) @ Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
thf(2,axiom,
! [Y: $i] : ( r @ Y @ zero @ ( succ @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
thf(3,conjecture,
? [Z3: $i,Z2: $i,Z1: $i,Z0: $i] :
( ( r @ zero @ zero @ Z3 )
& ( r @ zero @ Z3 @ Z2 )
& ( r @ zero @ Z2 @ Z1 )
& ( r @ zero @ Z1 @ Z0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
thf(4,negated_conjecture,
( ( ? [Z3: $i,Z2: $i,Z1: $i,Z0: $i] :
( ( r @ zero @ zero @ Z3 )
& ( r @ zero @ Z3 @ Z2 )
& ( r @ zero @ Z2 @ Z1 )
& ( r @ zero @ Z1 @ Z0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ? [Z3: $i,Z2: $i,Z1: $i,Z0: $i] :
( ( r @ zero @ zero @ Z3 )
& ( r @ zero @ Z3 @ Z2 )
& ( r @ zero @ Z2 @ Z1 )
& ( r @ zero @ Z1 @ Z0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [Y: $i,X: $i,Z: $i,Z1: $i] :
( ( r @ Y @ X @ Z )
=> ( ( r @ Z @ X @ Z1 )
=> ( r @ Y @ ( succ @ X ) @ Z1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [Y: $i] : ( r @ Y @ zero @ ( succ @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ~ ? [Z3: $i,Z2: $i,Z1: $i,Z0: $i] :
( ( r @ zero @ zero @ Z3 )
& ( r @ zero @ Z3 @ Z2 )
& ( r @ zero @ Z2 @ Z1 )
& ( r @ zero @ Z1 @ Z0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [Z3: $i,Z2: $i,Z1: $i] :
( ~ ( r @ zero @ zero @ Z3 )
| ~ ( r @ zero @ Z3 @ Z2 )
| ~ ( r @ zero @ Z2 @ Z1 )
| ! [Z0: $i] :
~ ( r @ zero @ Z1 @ Z0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( r @ Y @ X @ Z )
| ! [Z1: $i] :
( ~ ( r @ Z @ X @ Z1 )
| ( r @ Y @ ( succ @ X ) @ Z1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [Y: $i] : ( r @ Y @ zero @ ( succ @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(12,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ~ ( r @ Y @ X @ Z )
| ! [Z1: $i] :
( ~ ( r @ Z @ X @ Z1 )
| ( r @ Y @ ( succ @ X ) @ Z1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [Z3: $i,Z2: $i,Z1: $i] :
( ~ ( r @ zero @ zero @ Z3 )
| ~ ( r @ zero @ Z3 @ Z2 )
| ~ ( r @ zero @ Z2 @ Z1 )
| ! [Z0: $i] :
~ ( r @ zero @ Z1 @ Z0 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
! [SV1: $i] :
( ( r @ SV1 @ zero @ ( succ @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ( r @ SV2 @ SY9 @ SY10 )
| ! [SY11: $i] :
( ~ ( r @ SY10 @ SY9 @ SY11 )
| ( r @ SV2 @ ( succ @ SY9 ) @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
! [SV3: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ~ ( r @ zero @ zero @ SV3 )
| ~ ( r @ zero @ SV3 @ SY12 )
| ~ ( r @ zero @ SY12 @ SY13 )
| ! [Z0: $i] :
~ ( r @ zero @ SY13 @ Z0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY15: $i] :
( ~ ( r @ SV2 @ SV4 @ SY15 )
| ! [SY16: $i] :
( ~ ( r @ SY15 @ SV4 @ SY16 )
| ( r @ SV2 @ ( succ @ SV4 ) @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY17: $i] :
( ~ ( r @ zero @ zero @ SV3 )
| ~ ( r @ zero @ SV3 @ SV5 )
| ~ ( r @ zero @ SV5 @ SY17 )
| ! [Z0: $i] :
~ ( r @ zero @ SY17 @ Z0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ~ ( r @ SV2 @ SV4 @ SV6 )
| ! [SY19: $i] :
( ~ ( r @ SV6 @ SV4 @ SY19 )
| ( r @ SV2 @ ( succ @ SV4 ) @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ~ ( r @ zero @ zero @ SV3 )
| ~ ( r @ zero @ SV3 @ SV5 )
| ~ ( r @ zero @ SV5 @ SV7 )
| ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( r @ SV2 @ SV4 @ SV6 ) )
= $true )
| ( ( ! [SY19: $i] :
( ~ ( r @ SV6 @ SV4 @ SY19 )
| ( r @ SV2 @ ( succ @ SV4 ) @ SY19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( r @ zero @ zero @ SV3 )
| ~ ( r @ zero @ SV3 @ SV5 )
| ~ ( r @ zero @ SV5 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( r @ SV2 @ SV4 @ SV6 )
= $false )
| ( ( ! [SY19: $i] :
( ~ ( r @ SV6 @ SV4 @ SY19 )
| ( r @ SV2 @ ( succ @ SV4 ) @ SY19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( r @ zero @ zero @ SV3 )
| ~ ( r @ zero @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( r @ zero @ SV5 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV8: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( r @ SV6 @ SV4 @ SV8 )
| ( r @ SV2 @ ( succ @ SV4 ) @ SV8 ) )
= $true )
| ( ( r @ SV2 @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( r @ zero @ zero @ SV3 ) )
= $true )
| ( ( ~ ( r @ zero @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( r @ zero @ SV5 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i,SV8: $i,SV4: $i,SV6: $i] :
( ( ( ~ ( r @ SV6 @ SV4 @ SV8 ) )
= $true )
| ( ( r @ SV2 @ ( succ @ SV4 ) @ SV8 )
= $true )
| ( ( r @ SV2 @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( r @ zero @ zero @ SV3 )
= $false )
| ( ( ~ ( r @ zero @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( r @ zero @ SV5 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV8: $i,SV4: $i,SV6: $i] :
( ( ( r @ SV6 @ SV4 @ SV8 )
= $false )
| ( ( r @ SV2 @ ( succ @ SV4 ) @ SV8 )
= $true )
| ( ( r @ SV2 @ SV4 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( r @ zero @ SV3 @ SV5 )
= $false )
| ( ( r @ zero @ zero @ SV3 )
= $false )
| ( ( ~ ( r @ zero @ SV5 @ SV7 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV7: $i,SV5: $i] :
( ( ( r @ zero @ SV5 @ SV7 )
= $false )
| ( ( r @ zero @ zero @ SV3 )
= $false )
| ( ( r @ zero @ SV3 @ SV5 )
= $false )
| ( ( ! [SY20: $i] :
~ ( r @ zero @ SV7 @ SY20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV5: $i,SV3: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( r @ zero @ SV7 @ SV9 ) )
= $true )
| ( ( r @ zero @ SV3 @ SV5 )
= $false )
| ( ( r @ zero @ zero @ SV3 )
= $false )
| ( ( r @ zero @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
! [SV5: $i,SV3: $i,SV9: $i,SV7: $i] :
( ( ( r @ zero @ SV7 @ SV9 )
= $false )
| ( ( r @ zero @ SV3 @ SV5 )
= $false )
| ( ( r @ zero @ zero @ SV3 )
= $false )
| ( ( r @ zero @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,33,29]) ).
thf(35,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:30:09 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 2
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 .
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:34,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 35 ****
% 0.07/0.22 %**** clause counter: 34 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:34,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------