%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV131^5 : 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 : 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 10:49:36 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 260 ( 52 ~; 33 |; 9 &; 133 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 ^; 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > $o ).
thf(tp_sK2_SY6,type,
sK2_SY6: a ).
thf(tp_sK3_SY11,type,
sK3_SY11: a ).
thf(tp_sK4_SX0,type,
sK4_SX0: a > $o ).
thf(1,conjecture,
! [Xr: a > a > $o,Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz: a] :
( ( ( Xr @ Xy0 @ Xz )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM202_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > $o,Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz: a] :
( ( ( Xr @ Xy0 @ Xz )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > $o,Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xx0: a > $o] :
( ! [Xy0: a,Xz: a] :
( ( ( Xr @ Xy0 @ Xz )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY6: a,SY7: a] :
( ( sK1_Xr @ SY6 @ SY7 )
=> ! [SY8: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY8 @ SY9 ) )
=> ( SY8 @ SY10 ) )
=> ( ( SY8 @ SY6 )
=> ( SY8 @ SY7 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY11: a] :
( ( sK1_Xr @ sK2_SY6 @ SY11 )
=> ! [SY12: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY12 @ SY9 ) )
=> ( SY12 @ SY10 ) )
=> ( ( SY12 @ sK2_SY6 )
=> ( SY12 @ SY11 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( sK1_Xr @ sK2_SY6 @ sK3_SY11 )
=> ! [SY15: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY15 @ SY9 ) )
=> ( SY15 @ SY10 ) )
=> ( ( SY15 @ sK2_SY6 )
=> ( SY15 @ sK3_SY11 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( sK1_Xr @ sK2_SY6 @ sK3_SY11 )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY15: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY15 @ SY9 ) )
=> ( SY15 @ SY10 ) )
=> ( ( SY15 @ sK2_SY6 )
=> ( SY15 @ sK3_SY11 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SY15: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY15 @ SY9 ) )
=> ( SY15 @ SY10 ) )
=> ( ( SY15 @ sK2_SY6 )
=> ( SY15 @ sK3_SY11 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( sK1_Xr @ sK2_SY6 @ sK3_SY11 )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SY15: a > $o] :
( ! [SY9: a,SY10: a] :
( ( ( sK1_Xr @ SY9 @ SY10 )
& ( SY15 @ SY9 ) )
=> ( SY15 @ SY10 ) )
=> ( ( SY15 @ sK2_SY6 )
=> ( SY15 @ sK3_SY11 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK2_SY6 )
| ( SX0 @ sK3_SY11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX1 @ SX2 )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ SX2 ) )
| ~ ( SX0 @ sK2_SY6 )
| ( SX0 @ sK3_SY11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ! [SY18: a,SY19: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY18 @ SY19 )
| ~ ( sK4_SX0 @ SY18 ) )
| ( sK4_SX0 @ SY19 ) )
| ~ ( sK4_SX0 @ sK2_SY6 )
| ( sK4_SX0 @ sK3_SY11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( ~ ! [SY18: a,SY19: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY18 @ SY19 )
| ~ ( sK4_SX0 @ SY18 ) )
| ( sK4_SX0 @ SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( sK4_SX0 @ sK2_SY6 )
| ( sK4_SX0 @ sK3_SY11 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SY18: a,SY19: a] :
( ~ ~ ( ~ ( sK1_Xr @ SY18 @ SY19 )
| ~ ( sK4_SX0 @ SY18 ) )
| ( sK4_SX0 @ SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK4_SX0 @ sK2_SY6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK4_SX0 @ sK3_SY11 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: a] :
( ( ! [SY20: a] :
( ~ ~ ( ~ ( sK1_Xr @ SV1 @ SY20 )
| ~ ( sK4_SX0 @ SV1 ) )
| ( sK4_SX0 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK4_SX0 @ sK2_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: a,SV1: a] :
( ( ~ ~ ( ~ ( sK1_Xr @ SV1 @ SV2 )
| ~ ( sK4_SX0 @ SV1 ) )
| ( sK4_SX0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: a,SV1: a] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ SV1 @ SV2 )
| ~ ( sK4_SX0 @ SV1 ) ) )
= $true )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(24,plain,
! [SV2: a,SV1: a] :
( ( ( ~ ( ~ ( sK1_Xr @ SV1 @ SV2 )
| ~ ( sK4_SX0 @ SV1 ) ) )
= $false )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV2: a,SV1: a] :
( ( ( ~ ( sK1_Xr @ SV1 @ SV2 )
| ~ ( sK4_SX0 @ SV1 ) )
= $true )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(26,plain,
! [SV2: a,SV1: a] :
( ( ( ~ ( sK1_Xr @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( sK4_SX0 @ SV1 ) )
= $true )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV2: a,SV1: a] :
( ( ( sK1_Xr @ SV1 @ SV2 )
= $false )
| ( ( ~ ( sK4_SX0 @ SV1 ) )
= $true )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV2: a,SV1: a] :
( ( ( sK4_SX0 @ SV1 )
= $false )
| ( ( sK1_Xr @ SV1 @ SV2 )
= $false )
| ( ( sK4_SX0 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,28,21,19]) ).
thf(30,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV131^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.20 % Computer : n015.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Oct 6 15:44:28 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.24
% 0.12/0.24 No.of.Axioms: 0
% 0.12/0.24
% 0.12/0.24 Length.of.Defs: 0
% 0.12/0.24
% 0.12/0.24 Contains.Choice.Funs: false
% 0.12/0.24
% 0.12/0.24 ********************************
% 0.12/0.24 * All subproblems solved! *
% 0.12/0.24 ********************************
% 0.12/0.24 % 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:29,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.24
% 0.12/0.24 %**** Beginning of derivation protocol ****
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24
% 0.12/0.24 %**** End of derivation protocol ****
% 0.12/0.24 %**** no. of clauses in derivation: 30 ****
% 0.12/0.24 %**** clause counter: 29 ****
% 0.12/0.24
% 0.12/0.24 % 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:29,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------