%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV257^5 : 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 : 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 10:49:50 AM UTC 2026
% Result : Theorem 92.32s 15.61s
% Output : CNFRefutation 92.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 170 ( 39 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 261 ( 84 ~; 34 |; 20 &; 109 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 29 ^; 33 !; 6 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cOPEN,type,
cOPEN: ( a > $o ) > $o ).
thf(tp_sK10_E,type,
sK10_E: a ).
thf(tp_sK11_E,type,
sK11_E: a ).
thf(tp_sK12_E,type,
sK12_E: a ).
thf(tp_sK13_SY74,type,
sK13_SY74: a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK2_E,type,
sK2_E: ( ( a > $o ) > a > $o ) > a ).
thf(tp_sK3_E,type,
sK3_E: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK4_SV52,type,
sK4_SV52: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK5_SX0,type,
sK5_SX0: ( ( a > $o ) > a > a ) > a > $o ).
thf(tp_sK6_SX0,type,
sK6_SX0: ( ( a > $o ) > a > ( a > $o ) > $o ) > a > $o ).
thf(tp_sK7_SX0,type,
sK7_SX0: ( ( a > $o ) > a > a ) > a > $o ).
thf(tp_sK8_SX0,type,
sK8_SX0: ( ( a > $o ) > a > $o ) > a > $o ).
thf(tp_sK9_E,type,
sK9_E: a ).
thf(1,conjecture,
( ( ( cOPEN
@ ^ [Xy: a] : $true )
& ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
& ! [Y: a > $o,Z: a > $o] :
( ( ( cOPEN @ Y )
& ( cOPEN @ Z ) )
=> ( cOPEN
@ ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( cOPEN
@ ^ [Xy: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM625_pme) ).
thf(2,negated_conjecture,
( ( ( ( cOPEN
@ ^ [Xy: a] : $true )
& ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
& ! [Y: a > $o,Z: a > $o] :
( ( ( cOPEN @ Y )
& ( cOPEN @ Z ) )
=> ( cOPEN
@ ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( cOPEN
@ ^ [Xy: a] : $false ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( cOPEN
@ ^ [Xy: a] : $true )
& ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) )
& ! [Y: a > $o,Z: a > $o] :
( ( ( cOPEN @ Y )
& ( cOPEN @ Z ) )
=> ( cOPEN
@ ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( cOPEN
@ ^ [Xy: a] : $false ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(5,plain,
( ( ! [K: ( a > $o ) > $o] :
( ! [Xx: a > $o] :
( ( K @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( cOPEN
@ ^ [Xy: a] : $false )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ( cOPEN
@ ^ [Xy: a] : $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [K: ( a > $o ) > $o] :
( ( ( K @ ( sK1_Xx @ K ) )
& ~ ( cOPEN @ ( sK1_Xx @ K ) ) )
| ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [K: ( a > $o ) > $o] :
( ( ( K @ ( sK1_Xx @ K ) )
& ~ ( cOPEN @ ( sK1_Xx @ K ) ) )
| ( cOPEN
@ ^ [Xx: a] :
? [S: a > $o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ ( cOPEN
@ ^ [Xy: a] : $false ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ( ~ ( SX0 @ ( sK1_Xx @ SX0 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SX0 ) ) )
| ( cOPEN
@ ^ [SX1: a] :
~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(17,plain,
( ( cOPEN
@ ^ [Xy: a] : $false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: ( a > $o ) > $o] :
( ( ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) )
| ( cOPEN
@ ^ [SY9: a] :
~ ! [SY10: a > $o] :
~ ~ ( ~ ( SV1 @ SY10 )
| ~ ( SY10 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) ) )
= $true )
| ( ( cOPEN
@ ^ [SY9: a] :
~ ! [SY10: a > $o] :
~ ~ ( ~ ( SV1 @ SY10 )
| ~ ( SY10 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) )
| ~ ~ ( cOPEN @ ( sK1_Xx @ SV1 ) ) )
= $false )
| ( ( cOPEN
@ ^ [SY9: a] :
~ ! [SY10: a > $o] :
~ ~ ( ~ ( SV1 @ SY10 )
| ~ ( SY10 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) ) )
= $false )
| ( ( cOPEN
@ ^ [SY9: a] :
~ ! [SY10: a > $o] :
~ ~ ( ~ ( SV1 @ SY10 )
| ~ ( SY10 @ SY9 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( SV1 @ ( sK1_Xx @ SV1 ) )
= $true )
| ( ( cOPEN
@ ^ [SY9: a] :
~ ! [SY10: a > $o] :
~ ~ ( ~ ( SV1 @ SY10 )
| ~ ( SY10 @ SY9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(33,plain,
( ( $false = $true )
| ( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[27:[bind(SV1,$thf( ^ [SV6: a > $o] : $false ))]]) ).
thf(201,plain,
( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= $true ),
inference(sim,[status(thm)],[33]) ).
thf(205,plain,
( ( ( cOPEN
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ $false
| ~ ( SX1 @ SX0 ) ) )
= ( cOPEN
@ ^ [Xy: a] : $false ) )
= $false ),
inference(res,[status(thm)],[201,17]) ).
thf(206,plain,
( ( ( ~ ! [SY74: a > $o] :
~ ~ ( ~ $false
| ~ ( SY74 @ sK12_E ) ) )
= $true )
| ( $false = $true ) ),
inference(extuni,[status(esa)],[205]) ).
thf(209,plain,
( ( ( ! [SY74: a > $o] :
~ ~ ( ~ $false
| ~ ( SY74 @ sK12_E ) ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(211,plain,
( ( ( ~ ~ ( ~ $false
| ~ ( sK13_SY74 @ sK12_E ) ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(213,plain,
( ( ( ~ ( ~ $false
| ~ ( sK13_SY74 @ sK12_E ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(215,plain,
( ( ( ~ $false
| ~ ( sK13_SY74 @ sK12_E ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(217,plain,
( ( ( ~ $false ) = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(220,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(223,plain,
$false = $true,
inference(sim,[status(thm)],[220]) ).
thf(224,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV257^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n002.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 15:46:27 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
% 92.32/15.61
% 92.32/15.61 No.of.Axioms: 0
% 92.32/15.61
% 92.32/15.61 Length.of.Defs: 0
% 92.32/15.61
% 92.32/15.61 Contains.Choice.Funs: false
% 92.32/15.61 ..............eprover: CPU time limit exceeded, terminating
% 92.32/15.61
% 92.32/15.61
% 92.32/15.61 ********************************
% 92.32/15.61 * All subproblems solved! *
% 92.32/15.61 ********************************
% 92.32/15.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:223,loop_count:3,foatp_calls:2,translation:fof_experiment)
% 92.32/15.61
% 92.32/15.61 %**** Beginning of derivation protocol ****
% 92.32/15.61 % SZS output start CNFRefutation
% See solution above
% 92.32/15.62
% 92.32/15.62 %**** End of derivation protocol ****
% 92.32/15.62 %**** no. of clauses in derivation: 28 ****
% 92.32/15.62 %**** clause counter: 223 ****
% 92.32/15.62
% 92.32/15.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:223,loop_count:3,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------