%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET199^5 : 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 : n004.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 10:39:54 AM UTC 2026
% Result : Theorem 0.13s 0.21s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 33 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 164 ( 13 ~; 24 |; 6 &; 90 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 47 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY6,type,
sK2_SY6: a > $o ).
thf(tp_sK3_SY11,type,
sK3_SY11: a > $o ).
thf(tp_sK4_SX0,type,
sK4_SX0: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( Z @ Xx )
=> ( X @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( Y @ Xx ) ) )
=> ! [Xx: a] :
( ( Z @ Xx )
=> ( ( X @ Xx )
| ( Y @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_39_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( Z @ Xx )
=> ( X @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( Y @ Xx ) ) )
=> ! [Xx: a] :
( ( Z @ Xx )
=> ( ( X @ Xx )
| ( Y @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( Z @ Xx )
=> ( X @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( Y @ Xx ) ) )
=> ! [Xx: a] :
( ( Z @ Xx )
=> ( ( X @ Xx )
| ( Y @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY6: a > $o,SY7: a > $o] :
( ( ! [SY8: a] :
( ( SY7 @ SY8 )
=> ( sK1_X @ SY8 ) )
& ! [Xx: a] :
( ( SY7 @ Xx )
=> ( SY6 @ Xx ) ) )
=> ! [SY10: a] :
( ( SY7 @ SY10 )
=> ( ( sK1_X @ SY10 )
| ( SY6 @ SY10 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY11: a > $o] :
( ( ! [SY8: a] :
( ( SY11 @ SY8 )
=> ( sK1_X @ SY8 ) )
& ! [SY13: a] :
( ( SY11 @ SY13 )
=> ( sK2_SY6 @ SY13 ) ) )
=> ! [SY14: a] :
( ( SY11 @ SY14 )
=> ( ( sK1_X @ SY14 )
| ( sK2_SY6 @ SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY15: a] :
( ( sK3_SY11 @ SY15 )
=> ( sK1_X @ SY15 ) )
& ! [SY16: a] :
( ( sK3_SY11 @ SY16 )
=> ( sK2_SY6 @ SY16 ) ) )
=> ! [SY17: a] :
( ( sK3_SY11 @ SY17 )
=> ( ( sK1_X @ SY17 )
| ( sK2_SY6 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY15: a] :
( ( sK3_SY11 @ SY15 )
=> ( sK1_X @ SY15 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY16: a] :
( ( sK3_SY11 @ SY16 )
=> ( sK2_SY6 @ SY16 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY17: a] :
( ( sK3_SY11 @ SY17 )
=> ( ( sK1_X @ SY17 )
| ( sK2_SY6 @ SY17 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY17: a] :
( ( sK3_SY11 @ SY17 )
=> ( ( sK1_X @ SY17 )
| ( sK2_SY6 @ SY17 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY16: a] :
( ( sK3_SY11 @ SY16 )
=> ( sK2_SY6 @ SY16 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SY15: a] :
( ( sK3_SY11 @ SY15 )
=> ( sK1_X @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ ! [SY17: a] :
( ( sK3_SY11 @ SY17 )
=> ( ( sK1_X @ SY17 )
| ( sK2_SY6 @ SY17 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: a] :
( ~ ( sK3_SY11 @ SX0 )
| ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: a] :
( ~ ( sK3_SY11 @ SX0 )
| ( sK1_X @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: a] :
( ~ ( sK3_SY11 @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SX0: a] :
( ~ ( sK3_SY11 @ SX0 )
| ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: a] :
( ( ~ ( sK3_SY11 @ SV1 )
| ( sK1_X @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: a] :
( ( ~ ( sK3_SY11 @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( sK3_SY11 @ sK4_SX0 )
| ( sK1_X @ sK4_SX0 )
| ( sK2_SY6 @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV1: a] :
( ( ( ~ ( sK3_SY11 @ SV1 ) )
= $true )
| ( ( sK1_X @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: a] :
( ( ( ~ ( sK3_SY11 @ SV2 ) )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( sK3_SY11 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ( sK1_X @ sK4_SX0 )
| ( sK2_SY6 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV1: a] :
( ( ( sK3_SY11 @ SV1 )
= $false )
| ( ( sK1_X @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: a] :
( ( ( sK3_SY11 @ SV2 )
= $false )
| ( ( sK2_SY6 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( sK3_SY11 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( sK1_X @ sK4_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( sK2_SY6 @ sK4_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,29,28,27,26]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199^5 : 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
% 0.13/0.18 % Computer : n004.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Oct 6 14:35:24 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.21
% 0.13/0.21 No.of.Axioms: 0
% 0.13/0.21
% 0.13/0.21 Length.of.Defs: 0
% 0.13/0.21
% 0.13/0.21 Contains.Choice.Funs: false
% 0.13/0.21
% 0.13/0.21 ********************************
% 0.13/0.21 * All subproblems solved! *
% 0.13/0.21 ********************************
% 0.13/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.21
% 0.13/0.21 %**** Beginning of derivation protocol ****
% 0.13/0.21 % SZS output start CNFRefutation
% See solution above
% 0.13/0.21
% 0.13/0.21 %**** End of derivation protocol ****
% 0.13/0.21 %**** no. of clauses in derivation: 31 ****
% 0.13/0.21 %**** clause counter: 30 ****
% 0.13/0.21
% 0.13/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------