%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU864^5 : 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 : n012.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 10:49:08 AM UTC 2026
% Result : Theorem 0.09s 0.18s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 237 ( 117 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 182 ( 11 ~; 53 |; 4 &; 98 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 36 ^; 40 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: ( a > $o ) > $o ).
thf(tp_sK2_E,type,
sK2_E: a ).
thf(tp_sK3_E,type,
sK3_E: a ).
thf(tp_sK4_E,type,
sK4_E: a ).
thf(tp_sK5_E,type,
sK5_E: ( a > $o ) > a ).
thf(tp_t,type,
t: a ).
thf(1,conjecture,
! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx: a > $o] :
( ( X @ Xx )
=> ! [Xt_0: a] :
( ( t = Xt_0 )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt_0 = Xz ) ) ) ) ) )
=> ( X
@ ^ [Xy: a] : ( t = Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDOMLEMMA1_pme) ).
thf(2,negated_conjecture,
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx: a > $o] :
( ( X @ Xx )
=> ! [Xt_0: a] :
( ( t = Xt_0 )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt_0 = Xz ) ) ) ) ) )
=> ( X
@ ^ [Xy: a] : ( t = Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx: a > $o] :
( ( X @ Xx )
=> ! [Xt_0: a] :
( ( t = Xt_0 )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt_0 = Xz ) ) ) ) ) )
=> ( X
@ ^ [Xy: a] : ( t = Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ( sK1_X
@ ^ [Xy: a] : $false )
& ! [SY7: a > $o] :
( ( sK1_X @ SY7 )
=> ! [SY8: a] :
( ( t = SY8 )
=> ( sK1_X
@ ^ [Xz: a] :
( ( SY7 @ Xz )
| ( SY8 = Xz ) ) ) ) ) )
=> ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( sK1_X
@ ^ [Xy: a] : $false )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY7: a > $o] :
( ( sK1_X @ SY7 )
=> ! [SY8: a] :
( ( t = SY8 )
=> ( sK1_X
@ ^ [Xz: a] :
( ( SY7 @ Xz )
| ( SY8 = Xz ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY7: a > $o] :
( ( sK1_X @ SY7 )
=> ! [SY8: a] :
( ( t = SY8 )
=> ( sK1_X
@ ^ [Xz: a] :
( ( SY7 @ Xz )
| ( SY8 = Xz ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( sK1_X
@ ^ [Xy: a] : $false )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ~ ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SX0: a > $o] :
( ~ ( sK1_X @ SX0 )
| ! [SX1: a] :
( ( t != SX1 )
| ( sK1_X
@ ^ [SX2: a] :
( ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(13,plain,
( ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: a > $o] :
( ( ~ ( sK1_X @ SV1 )
| ! [SY11: a] :
( ( t != SY11 )
| ( sK1_X
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY11 = SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: a > $o] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $true )
| ( ( ! [SY11: a] :
( ( t != SY11 )
| ( sK1_X
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY11 = SY12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV1: a > $o] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( ! [SY11: a] :
( ( t != SY11 )
| ( sK1_X
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY11 = SY12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV1: a > $o,SV2: a] :
( ( ( ( t != SV2 )
| ( sK1_X
@ ^ [SY13: a] :
( ( SV1 @ SY13 )
| ( SV2 = SY13 ) ) ) )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV1: a > $o,SV2: a] :
( ( ( t != SV2 )
= $true )
| ( ( sK1_X
@ ^ [SY13: a] :
( ( SV1 @ SY13 )
| ( SV2 = SY13 ) ) )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV1: a > $o,SV2: a] :
( ( ( t = SV2 )
= $false )
| ( ( sK1_X
@ ^ [SY13: a] :
( ( SV1 @ SY13 )
| ( SV2 = SY13 ) ) )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV1: a > $o] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( sK1_X
@ ^ [SX0: a] :
( ( SV1 @ SX0 )
| ( t = SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[19:[bind(SV2,$thf( t ))]]) ).
thf(21,plain,
( ( ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) )
= ( sK1_X
@ ^ [Xy: a] : $false ) )
= $false ),
inference(res,[status(thm)],[13,10]) ).
thf(22,plain,
( ( ( t = sK2_E )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[21]) ).
thf(24,plain,
( ( t = sK2_E )
= $true ),
inference(sim,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: a > $o] :
( ( ( sK1_X @ SV3 )
= $false )
| ( ( sK1_X
@ ^ [SX0: a] :
( ( SV3 @ SX0 )
| ( t = SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[20]) ).
thf(30,plain,
! [SV3: a > $o] :
( ( ( ( sK1_X
@ ^ [SX0: a] :
( ( SV3 @ SX0 )
| ( t = SX0 ) ) )
= ( sK1_X
@ ^ [Xy: a] : ( t = Xy ) ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false ) ),
inference(res,[status(thm)],[26,13]) ).
thf(31,plain,
! [SV3: a > $o] :
( ( ( ( sK1_X @ SV3 )
= ( sK1_X
@ ^ [Xy: a] : $false ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: a] :
( ( SV3 @ SX0 )
| ( t = SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[26,10]) ).
thf(32,plain,
( ( sK1_X
@ ^ [SX0: a] :
( $false
| ( t = SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[31:[bind(SV3,$thf( ^ [SX0: a] : $false ))]]) ).
thf(33,plain,
! [SV3: a > $o] :
( ( ( sK1_X @ SV3 )
= $false )
| ( ( ( SV3 @ ( sK5_E @ SV3 ) )
| ( t
= ( sK5_E @ SV3 ) ) )
= $true )
| ( ( t
= ( sK5_E @ SV3 ) )
= $true ) ),
inference(extuni,[status(esa)],[30]) ).
thf(34,plain,
! [SV3: a > $o] :
( ( ( sK1_X @ SV3 )
= $false )
| ( ( ( SV3 @ ( sK5_E @ SV3 ) )
| ( t
= ( sK5_E @ SV3 ) ) )
= $false )
| ( ( t
= ( sK5_E @ SV3 ) )
= $false ) ),
inference(extuni,[status(esa)],[30]) ).
thf(35,plain,
! [SV3: a > $o] :
( ( ( SV3 @ ( sK5_E @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( t
= ( sK5_E @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(36,plain,
! [SV3: a > $o] :
( ( ( t
= ( sK5_E @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( t
= ( sK5_E @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: a > $o] :
( ( ( SV3 @ ( sK5_E @ SV3 ) )
= $true )
| ( ( t
= ( sK5_E @ SV3 ) )
= $true )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( t
= ( sK5_E @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV3: a > $o] :
( ( ( t
= ( sK5_E @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: a > $o] :
( ( ( SV3 @ ( sK5_E @ SV3 ) )
= $true )
| ( ( t
= ( sK5_E @ SV3 ) )
= $true )
| ( ( sK1_X @ SV3 )
= $false ) ),
inference(sim,[status(thm)],[37]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,39,38,35,32,26,24,19,13]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU864^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:36:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18
% 0.09/0.18 No.of.Axioms: 0
% 0.09/0.18
% 0.09/0.18 Length.of.Defs: 0
% 0.09/0.18
% 0.09/0.18 Contains.Choice.Funs: false
% 0.09/0.18 .
% 0.09/0.18
% 0.09/0.18 ********************************
% 0.09/0.18 * All subproblems solved! *
% 0.09/0.18 ********************************
% 0.09/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:40,loop_count:5,foatp_calls:3,translation:fof_full)
% 0.09/0.18
% 0.09/0.18 %**** Beginning of derivation protocol ****
% 0.09/0.18 % SZS output start CNFRefutation
% See solution above
% 0.09/0.18
% 0.09/0.18 %**** End of derivation protocol ****
% 0.09/0.18 %**** no. of clauses in derivation: 36 ****
% 0.09/0.18 %**** clause counter: 40 ****
% 0.09/0.18
% 0.09/0.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,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:40,loop_count:5,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------