%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU884^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:49:10 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 81 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 197 ( 54 ~; 38 |; 12 &; 81 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 37 !; 8 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cR,type,
cR: a > $o ).
thf(tp_cS,type,
cS: a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_Xt,type,
sK2_Xt: a > a ).
thf(1,conjecture,
( ! [Xx: a] :
( ? [Xt: a] :
( ( cR @ Xt )
& ( Xx = Xt ) )
=> ? [Xt: a] :
( ( cS @ Xt )
& ( Xx = Xt ) ) )
=> ! [Xx: a] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM30B_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] :
( ? [Xt: a] :
( ( cR @ Xt )
& ( Xx = Xt ) )
=> ? [Xt: a] :
( ( cS @ Xt )
& ( Xx = Xt ) ) )
=> ! [Xx: a] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a] :
( ? [Xt: a] :
( ( cR @ Xt )
& ( Xx = Xt ) )
=> ? [Xt: a] :
( ( cS @ Xt )
& ( Xx = Xt ) ) )
=> ! [Xx: a] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: a] :
( ? [Xt: a] :
( ( cR @ Xt )
& ( Xx = Xt ) )
=> ? [Xt: a] :
( ( cS @ Xt )
& ( Xx = Xt ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: a] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( cR @ sK1_Xx )
& ~ ( cS @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: a] :
( ! [Xt: a] :
( ( Xx != Xt )
| ~ ( cR @ Xt ) )
| ( ( Xx
= ( sK2_Xt @ Xx ) )
& ( cS @ ( sK2_Xt @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: a] :
( ! [Xt: a] :
( ( Xx != Xt )
| ~ ( cR @ Xt ) )
| ( ( Xx
= ( sK2_Xt @ Xx ) )
& ( cS @ ( sK2_Xt @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( cR @ sK1_Xx )
& ~ ( cS @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: a] :
( ! [SX1: a] :
( ( SX0 != SX1 )
| ~ ( cR @ SX1 ) )
| ~ ( ( SX0
!= ( sK2_Xt @ SX0 ) )
| ~ ( cS @ ( sK2_Xt @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ( cR @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: a] :
( ( ! [SY4: a] :
( ( SV1 != SY4 )
| ~ ( cR @ SY4 ) )
| ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( cR @ sK1_Xx )
| ~ ~ ( cS @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: a] :
( ( ( ! [SY4: a] :
( ( SV1 != SY4 )
| ~ ( cR @ SY4 ) ) )
= $true )
| ( ( ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( cR @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( cS @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: a,SV1: a] :
( ( ( ( SV1 != SV2 )
| ~ ( cR @ SV2 ) )
= $true )
| ( ( ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( cR @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( cS @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: a,SV1: a] :
( ( ( SV1 != SV2 )
= $true )
| ( ( ~ ( cR @ SV2 ) )
= $true )
| ( ( ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( cS @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: a,SV1: a] :
( ( ( SV1 = SV2 )
= $false )
| ( ( ~ ( cR @ SV2 ) )
= $true )
| ( ( ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: a,SV2: a] :
( ( ( cR @ SV2 )
= $false )
| ( ( SV1 = SV2 )
= $false )
| ( ( ~ ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV2: a,SV1: a] :
( ( ( ( SV1
!= ( sK2_Xt @ SV1 ) )
| ~ ( cS @ ( sK2_Xt @ SV1 ) ) )
= $false )
| ( ( SV1 = SV2 )
= $false )
| ( ( cR @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV2: a,SV1: a] :
( ( ( SV1
!= ( sK2_Xt @ SV1 ) )
= $false )
| ( ( SV1 = SV2 )
= $false )
| ( ( cR @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV2: a,SV1: a] :
( ( ( ~ ( cS @ ( sK2_Xt @ SV1 ) ) )
= $false )
| ( ( SV1 = SV2 )
= $false )
| ( ( cR @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: a,SV1: a] :
( ( ( SV1
= ( sK2_Xt @ SV1 ) )
= $true )
| ( ( SV1 = SV2 )
= $false )
| ( ( cR @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: a,SV1: a] :
( ( ( cS @ ( sK2_Xt @ SV1 ) )
= $true )
| ( ( SV1 = SV2 )
= $false )
| ( ( cR @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,29,28,22]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU884^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:40:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 31 ****
% 0.08/0.23 %**** clause counter: 30 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------