%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV162^5 : 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 : n016.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 10:49:40 AM UTC 2026
% Result : Theorem 0.27s 0.32s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 31 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 158 ( 12 ~; 4 |; 0 &; 132 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 151 ( 88 ^; 63 !; 0 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: ( a > a > a ) > a ).
thf(tp_sK3_SX0,type,
sK3_SX0: a ).
thf(tp_sK4_SY20,type,
sK4_SY20: a ).
thf(1,conjecture,
! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
<=> ! [Xp: ( a > a > a ) > a] :
( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM184_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
<=> ! [Xp: ( a > a > a ) > a] :
( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
<=> ! [Xp: ( a > a > a ) > a] :
( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
<=> ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
=> ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
=> ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
=> ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 )
| ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 )
| ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( sK1_Xr
@ ( sK2_SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( sK2_SX0
@ ^ [SX1: a,SX2: a] : SX2 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV1: a] :
( ( ! [SY19: a] : ( sK1_Xr @ SV1 @ SY19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV2: a,SV1: a] :
( ( sK1_Xr @ SV1 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,17]) ).
thf(19,plain,
( ( ~ ( ! [SY10: ( a > a > a ) > a] :
( sK1_Xr
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xx )
@ ( SY10
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ! [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) )
| ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) )
| ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
( ( ~ ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [SX0: a,SX1: a] : ( sK1_Xr @ SX0 @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [SX0: ( a > a > a ) > a] :
( sK1_Xr
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SX0
@ ^ [SX1: a,SX2: a] : SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [SY20: a] : ( sK1_Xr @ sK3_SX0 @ SY20 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(26,plain,
! [SV3: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SV3
@ ^ [SX1: a,SX2: a] : SX1 )
@ ( SV3
@ ^ [SX1: a,SX2: a] : SX2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( sK1_Xr @ sK3_SX0 @ sK4_SY20 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(28,plain,
! [SV4: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SV4
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV4
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $true ),
inference(rename,[status(thm)],[26]) ).
thf(52,plain,
! [SV34: ( a > a > a ) > a] :
( ( sK1_Xr
@ ( SV34
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV34
@ ^ [SX0: a,SX1: a] : SX1 ) )
= $true ),
inference(rename,[status(thm)],[28]) ).
thf(53,plain,
! [SV34: ( a > a > a ) > a] :
( ( ( sK1_Xr
@ ( SV34
@ ^ [SX0: a,SX1: a] : SX0 )
@ ( SV34
@ ^ [SX0: a,SX1: a] : SX1 ) )
= ( sK1_Xr @ sK3_SX0 @ sK4_SY20 ) )
= $false ),
inference(res,[status(thm)],[52,27]) ).
thf(54,plain,
$false = $true,
inference(extuni,[status(esa)],[53:[bind(SV34,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ ( SX0 @ ( SX0 @ sK3_SX0 @ ( SV85 @ SX0 ) ) @ ( SV65 @ SX0 ) ) @ ( SV41 @ SX0 ) ) @ sK4_SY20 ) ))]]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV162^5 : 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
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:46:59 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.32
% 0.27/0.32 No.of.Axioms: 0
% 0.27/0.32
% 0.27/0.32 Length.of.Defs: 0
% 0.27/0.32
% 0.27/0.32 Contains.Choice.Funs: false
% 0.27/0.32 .
% 0.27/0.32
% 0.27/0.32 ********************************
% 0.27/0.32 * All subproblems solved! *
% 0.27/0.32 ********************************
% 0.27/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:54,loop_count:6,foatp_calls:3,translation:fof_full)
% 0.27/0.32
% 0.27/0.32 %**** Beginning of derivation protocol ****
% 0.27/0.32 % SZS output start CNFRefutation
% See solution above
% 0.27/0.32
% 0.27/0.32 %**** End of derivation protocol ****
% 0.27/0.32 %**** no. of clauses in derivation: 32 ****
% 0.27/0.32 %**** clause counter: 54 ****
% 0.27/0.32
% 0.27/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:54,loop_count:6,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------