%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU858^5 : 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 10:49:08 AM UTC 2026
% Result : Theorem 0.06s 0.21s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 83 ( 6 ~; 17 |; 4 &; 47 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 25 ^; 25 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xw,type,
sK1_Xw: ( a > $o ) > $o ).
thf(1,conjecture,
! [Xw: ( a > $o ) > $o] :
( ( ( Xw
@ ^ [Xx: a] : $false )
& ! [Xr: a > $o,Xx: a] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: a] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw
@ ^ [Xx: a] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM163_pme) ).
thf(2,negated_conjecture,
( ( ! [Xw: ( a > $o ) > $o] :
( ( ( Xw
@ ^ [Xx: a] : $false )
& ! [Xr: a > $o,Xx: a] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: a] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw
@ ^ [Xx: a] : $false ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xw: ( a > $o ) > $o] :
( ( ( Xw
@ ^ [Xx: a] : $false )
& ! [Xr: a > $o,Xx: a] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: a] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw
@ ^ [Xx: a] : $false ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ( sK1_Xw
@ ^ [Xx: a] : $false )
& ! [SY7: a > $o,SY8: a] :
( ( sK1_Xw @ SY7 )
=> ( sK1_Xw
@ ^ [Xt: a] :
( ( SY7 @ Xt )
| ( Xt = SY8 ) ) ) ) )
=> ( sK1_Xw
@ ^ [Xx: a] : $false ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( sK1_Xw
@ ^ [Xx: a] : $false )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY7: a > $o,SY8: a] :
( ( sK1_Xw @ SY7 )
=> ( sK1_Xw
@ ^ [Xt: a] :
( ( SY7 @ Xt )
| ( Xt = SY8 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( sK1_Xw
@ ^ [Xx: a] : $false )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ( sK1_Xw
@ ^ [Xx: a] : $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY7: a > $o] :
( ~ ( sK1_Xw @ SY7 )
| ! [SY8: a] :
( sK1_Xw
@ ^ [Xt: a] :
( ( SY7 @ Xt )
| ( Xt = SY8 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(10,plain,
( ( ! [SY7: a > $o] :
( ~ ( sK1_Xw @ SY7 )
| ! [SY8: a] :
( sK1_Xw
@ ^ [Xt: a] :
( ( SY7 @ Xt )
| ( Xt = SY8 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( sK1_Xw
@ ^ [Xx: a] : $false )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(12,plain,
( ( ~ ( sK1_Xw
@ ^ [Xx: a] : $false ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
! [SV1: a > $o] :
( ( ~ ( sK1_Xw @ SV1 )
| ! [SY11: a] :
( sK1_Xw
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY12 = SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(14,plain,
( ( sK1_Xw
@ ^ [Xx: a] : $false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: a > $o] :
( ( ( ~ ( sK1_Xw @ SV1 ) )
= $true )
| ( ( ! [SY11: a] :
( sK1_Xw
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY12 = SY11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: a > $o] :
( ( ( sK1_Xw @ SV1 )
= $false )
| ( ( ! [SY11: a] :
( sK1_Xw
@ ^ [SY12: a] :
( ( SV1 @ SY12 )
| ( SY12 = SY11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: a,SV1: a > $o] :
( ( ( sK1_Xw
@ ^ [SY13: a] :
( ( SV1 @ SY13 )
| ( SY13 = SV2 ) ) )
= $true )
| ( ( sK1_Xw @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(18,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,17,14]) ).
thf(19,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU858^5 : 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
% 0.06/0.18 % Computer : n002.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 15:39:57 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.21
% 0.06/0.21 No.of.Axioms: 0
% 0.06/0.21
% 0.06/0.21 Length.of.Defs: 0
% 0.06/0.21
% 0.06/0.21 Contains.Choice.Funs: false
% 0.06/0.21
% 0.06/0.21 ********************************
% 0.06/0.21 * All subproblems solved! *
% 0.06/0.21 ********************************
% 0.06/0.21 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.21
% 0.06/0.21 %**** Beginning of derivation protocol ****
% 0.06/0.21 % SZS output start CNFRefutation
% See solution above
% 0.06/0.21
% 0.06/0.21 %**** End of derivation protocol ****
% 0.06/0.21 %**** no. of clauses in derivation: 19 ****
% 0.06/0.21 %**** clause counter: 18 ****
% 0.06/0.21
% 0.06/0.21 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:18,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------