%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO276^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 11:07:59 AM UTC 2026
% Result : Theorem 0.12s 0.21s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 238 ( 148 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 347 ( 38 ~; 60 |; 8 &; 228 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 105 ( 60 ^; 45 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cO,type,
cO: $i ).
thf(tp_cP,type,
cP: $i > $o ).
thf(tp_m,type,
m: $i ).
thf(tp_n,type,
n: $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_sK1_SY3,type,
sK1_SY3: ( $i > $i > $o ) > $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: ( $i > $i > $o ) > $i ).
thf(1,conjecture,
( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [Xx: $i,Xy: $i] :
( ( A @ Xx @ Xy )
=> ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I2) ).
thf(2,negated_conjecture,
( ( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [Xx: $i,Xy: $i] :
( ( A @ Xx @ Xy )
=> ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [Xx: $i,Xy: $i] :
( ( A @ Xx @ Xy )
=> ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [Xx: $i,Xy: $i] :
( ( A @ Xx @ Xy )
=> ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
=> ( A @ n @ m ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( cP @ n )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( cP @ m )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ( cP @ m ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( cP @ n )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [Xx: $i,Xy: $i] :
( ( A @ Xx @ Xy )
=> ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
=> ( A @ n @ m ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ( cP @ m ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ( SX0 @ cO @ cO )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 @ SX2 )
| ( SX0 @ ( s @ SX1 ) @ ( s @ SX2 ) ) ) )
| ( SX0 @ n @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( cP @ m )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i > $i > $o] :
( ( ~ ~ ( ~ ( SV1 @ cO @ cO )
| ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) )
| ( SV1 @ n @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ cO @ cO )
| ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) ) )
= $true )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ cO @ cO )
| ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) ) )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ cO @ cO )
| ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) )
= $true )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ cO @ cO ) )
= $true )
| ( ( ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) )
= $true )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ cO @ cO )
= $false )
| ( ( ~ ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) )
= $true )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY3: $i,SY4: $i] :
( ~ ( SV1 @ SY3 @ SY4 )
| ( SV1 @ ( s @ SY3 ) @ ( s @ SY4 ) ) ) )
= $false )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY5: $i] :
( ~ ( SV1 @ ( sK1_SY3 @ SV1 ) @ SY5 )
| ( SV1 @ ( s @ ( sK1_SY3 @ SV1 ) ) @ ( s @ SY5 ) ) ) )
= $false )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK1_SY3 @ SV1 ) @ ( sK2_SY5 @ SV1 ) )
| ( SV1 @ ( s @ ( sK1_SY3 @ SV1 ) ) @ ( s @ ( sK2_SY5 @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK1_SY3 @ SV1 ) @ ( sK2_SY5 @ SV1 ) ) )
= $false )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( s @ ( sK1_SY3 @ SV1 ) ) @ ( s @ ( sK2_SY5 @ SV1 ) ) )
= $false )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK1_SY3 @ SV1 ) @ ( sK2_SY5 @ SV1 ) )
= $true )
| ( ( SV1 @ cO @ cO )
= $false )
| ( ( SV1 @ n @ m )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ( s
@ ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( s
@ ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) ) )
= $false )
| ( ( cO = cO )
= $false )
| ( ( n = m )
= $true ) ),
inference(replace_andrewsEQ,[status(thm)],[23:[bind(SV1,$thf( ^ [SV3: $i] : ^ [SV2: $i] : ( SV3 = SV2 ) ))]]) ).
thf(26,plain,
( ( ( ( s
@ ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( s
@ ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) ) )
= $false )
| ( ( n = m )
= $true ) ),
inference(sim,[status(thm)],[25]) ).
thf(27,plain,
( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( cO = cO )
= $false )
| ( ( n = m )
= $true ) ),
inference(replace_andrewsEQ,[status(thm)],[24:[bind(SV1,$thf( ^ [SV5: $i] : ^ [SV4: $i] : ( SV5 = SV4 ) ))]]) ).
thf(28,plain,
( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( n = m )
= $true ) ),
inference(sim,[status(thm)],[27]) ).
thf(29,plain,
( ( ( n = m )
= $true )
| ( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( n = m ) )
= $false ) ),
inference(fac_restr,[status(thm)],[28]) ).
thf(30,plain,
( ( ( ~ ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
| ( n = m ) )
| ~ ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
!= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
| ( n != m ) ) )
= $false )
| ( ( n = m )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(31,plain,
( ( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( n = m ) )
= $false )
| ( ( n = m )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ~ ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
| ( n = m ) ) )
= $false )
| ( ( n = m )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
| ( n = m ) )
= $true )
| ( ( n = m )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( n = m )
= $true )
| ( ( n = m )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( ( n = m )
= $true )
| ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= m )
= $false )
| ( ( ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= n )
= $false ) ),
inference(extuni,[status(esa)],[31]) ).
thf(41,plain,
( ( ( n = m )
= $true )
| ( ( ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= m )
= $false )
| ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= n )
= $false ) ),
inference(extuni,[status(esa)],[31]) ).
thf(42,plain,
( ( ( n = m )
= $true )
| ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[26]) ).
thf(43,plain,
( ( ( ( sK1_SY3
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK2_SY5
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $true )
| ( ( n = m )
= $true ) ),
inference(sim,[status(thm)],[36]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,43,42,41,40,28,26,24,23,12]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO276^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.15 % Computer : n020.cluster.edu
% 0.12/0.15 % Model : x86_64 x86_64
% 0.12/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.15 % Memory : 8046.5625MB
% 0.12/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Oct 6 17:35:11 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.21
% 0.12/0.21 No.of.Axioms: 0
% 0.12/0.21
% 0.12/0.21 Length.of.Defs: 0
% 0.12/0.21
% 0.12/0.21 Contains.Choice.Funs: false
% 0.12/0.21
% 0.12/0.21 ********************************
% 0.12/0.21 * All subproblems solved! *
% 0.12/0.21 ********************************
% 0.12/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.12/0.21
% 0.12/0.21 %**** Beginning of derivation protocol ****
% 0.12/0.21 % SZS output start CNFRefutation
% See solution above
% 0.12/0.21
% 0.12/0.21 %**** End of derivation protocol ****
% 0.12/0.21 %**** no. of clauses in derivation: 40 ****
% 0.12/0.21 %**** clause counter: 44 ****
% 0.12/0.21
% 0.12/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------