%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU499^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n015.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 10:44:37 AM UTC 2026
% Result : Theorem 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 37 ( 27 unt; 0 typ; 1 def)
% Number of atoms : 181 ( 77 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 210 ( 69 ~; 38 |; 12 &; 75 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 3 ^; 49 !; 12 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i > $i ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(1,conjecture,
! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(2,negated_conjecture,
( ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,exu]) ).
thf(4,plain,
( ( ? [SY11: $i] :
( ( sK1_SY0 @ SY11 )
& ! [SY12: $i] :
( ( sK1_SY0 @ SY12 )
=> ( SY11 = SY12 ) ) )
=> ? [SY13: $i] :
( ( sK1_SY0 @ SY13 )
& ! [SY14: $i] :
( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [SY11: $i] :
( ( sK1_SY0 @ SY11 )
& ! [SY12: $i] :
( ( sK1_SY0 @ SY12 )
=> ( SY11 = SY12 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ? [SY13: $i] :
( ( sK1_SY0 @ SY13 )
& ! [SY14: $i] :
( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ? [SY13: $i] :
( ( sK1_SY0 @ SY13 )
& ! [SY14: $i] :
( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ? [SY11: $i] :
( ( sK1_SY0 @ SY11 )
& ! [SY12: $i] :
( ( sK1_SY0 @ SY12 )
=> ( SY11 = SY12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ? [SY13: $i] :
( ( sK1_SY0 @ SY13 )
& ! [SY14: $i] :
( ( sK1_SY0 @ SY14 )
=> ( SY13 = SY14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,exu]) ).
thf(11,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,exu]) ).
thf(12,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( sK1_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( sK1_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ( sK1_SY0 @ sK2_SX0 )
| ~ ! [SY15: $i] :
( ~ ( sK1_SY0 @ SY15 )
| ( sK2_SX0 = SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(15,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( sK1_SY0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( sK1_SY0 @ SX1 )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ( sK1_SY0 @ sK2_SX0 )
| ~ ! [SY15: $i] :
( ~ ( sK1_SY0 @ SY15 )
| ( sK2_SX0 = SY15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( sK1_SY0 @ SV1 )
| ~ ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 )
| ~ ! [SY15: $i] :
( ~ ( sK1_SY0 @ SY15 )
| ( sK2_SX0 = SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: $i] :
( ( ~ ( ~ ( sK1_SY0 @ SV1 )
| ~ ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SY15: $i] :
( ~ ( sK1_SY0 @ SY15 )
| ( sK2_SX0 = SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i] :
( ( ~ ( sK1_SY0 @ SV1 )
| ~ ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( sK1_SY0 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SY15: $i] :
( ~ ( sK1_SY0 @ SY15 )
| ( sK2_SX0 = SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 ) )
= $true )
| ( ( ~ ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i] :
( ( ~ ( sK1_SY0 @ SV2 )
| ( sK2_SX0 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: $i] :
( ( ( sK1_SY0 @ SV1 )
= $false )
| ( ( ~ ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 ) )
= $true )
| ( ( sK2_SX0 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ! [SY16: $i] :
( ~ ( sK1_SY0 @ SY16 )
| ( SV1 = SY16 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( sK1_SY0 @ SV2 )
= $false )
| ( ( sK2_SX0 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ ( sK3_SY16 @ SV1 ) )
| ( SV1
= ( sK3_SY16 @ SV1 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( ~ ( sK1_SY0 @ ( sK3_SY16 @ SV1 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(33,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK3_SY16 @ SV1 ) )
= $false )
| ( ( sK1_SY0 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i] :
( ( ( sK1_SY0 @ ( sK3_SY16 @ SV1 ) )
= $true )
| ( ( sK1_SY0 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,34,33,30]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU499^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n015.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 15:29:43 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 0
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 174
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 36 ****
% 0.07/0.21 %**** clause counter: 35 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------