%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET200^5 : 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 10:39:54 AM UTC 2026
% Result : Theorem 0.09s 0.19s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 210 ( 13 ~; 41 |; 7 &; 114 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY7,type,
sK2_SY7: a > $o ).
thf(tp_sK3_SY13,type,
sK3_SY13: a > $o ).
thf(tp_sK4_SY18,type,
sK4_SY18: a > $o ).
thf(tp_sK5_SX0,type,
sK5_SX0: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o,Z: a > $o,V: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( V @ Xx ) ) )
=> ! [Xx: a] :
( ( ( X @ Xx )
| ( Z @ Xx ) )
=> ( ( Y @ Xx )
| ( V @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_34_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o,V: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( V @ Xx ) ) )
=> ! [Xx: a] :
( ( ( X @ Xx )
| ( Z @ Xx ) )
=> ( ( Y @ Xx )
| ( V @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o,V: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( Z @ Xx )
=> ( V @ Xx ) ) )
=> ! [Xx: a] :
( ( ( X @ Xx )
| ( Z @ Xx ) )
=> ( ( Y @ Xx )
| ( V @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY7: a > $o,SY8: a > $o,SY9: a > $o] :
( ( ! [SY10: a] :
( ( sK1_X @ SY10 )
=> ( SY7 @ SY10 ) )
& ! [Xx: a] :
( ( SY8 @ Xx )
=> ( SY9 @ Xx ) ) )
=> ! [SY12: a] :
( ( ( sK1_X @ SY12 )
| ( SY8 @ SY12 ) )
=> ( ( SY7 @ SY12 )
| ( SY9 @ SY12 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: a > $o,SY14: a > $o] :
( ( ! [SY15: a] :
( ( sK1_X @ SY15 )
=> ( sK2_SY7 @ SY15 ) )
& ! [Xx: a] :
( ( SY13 @ Xx )
=> ( SY14 @ Xx ) ) )
=> ! [SY17: a] :
( ( ( sK1_X @ SY17 )
| ( SY13 @ SY17 ) )
=> ( ( sK2_SY7 @ SY17 )
| ( SY14 @ SY17 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY18: a > $o] :
( ( ! [SY15: a] :
( ( sK1_X @ SY15 )
=> ( sK2_SY7 @ SY15 ) )
& ! [SY20: a] :
( ( sK3_SY13 @ SY20 )
=> ( SY18 @ SY20 ) ) )
=> ! [SY21: a] :
( ( ( sK1_X @ SY21 )
| ( sK3_SY13 @ SY21 ) )
=> ( ( sK2_SY7 @ SY21 )
| ( SY18 @ SY21 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ! [SY15: a] :
( ( sK1_X @ SY15 )
=> ( sK2_SY7 @ SY15 ) )
& ! [SY23: a] :
( ( sK3_SY13 @ SY23 )
=> ( sK4_SY18 @ SY23 ) ) )
=> ! [SY24: a] :
( ( ( sK1_X @ SY24 )
| ( sK3_SY13 @ SY24 ) )
=> ( ( sK2_SY7 @ SY24 )
| ( sK4_SY18 @ SY24 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY15: a] :
( ( sK1_X @ SY15 )
=> ( sK2_SY7 @ SY15 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY23: a] :
( ( sK3_SY13 @ SY23 )
=> ( sK4_SY18 @ SY23 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SY24: a] :
( ( ( sK1_X @ SY24 )
| ( sK3_SY13 @ SY24 ) )
=> ( ( sK2_SY7 @ SY24 )
| ( sK4_SY18 @ SY24 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SY24: a] :
( ( ( sK1_X @ SY24 )
| ( sK3_SY13 @ SY24 ) )
=> ( ( sK2_SY7 @ SY24 )
| ( sK4_SY18 @ SY24 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY23: a] :
( ( sK3_SY13 @ SY23 )
=> ( sK4_SY18 @ SY23 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY15: a] :
( ( sK1_X @ SY15 )
=> ( sK2_SY7 @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ! [SY24: a] :
( ( ( sK1_X @ SY24 )
| ( sK3_SY13 @ SY24 ) )
=> ( ( sK2_SY7 @ SY24 )
| ( sK4_SY18 @ SY24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ! [SX0: a] :
( ~ ( ( sK1_X @ SX0 )
| ( sK3_SY13 @ SX0 ) )
| ( sK2_SY7 @ SX0 )
| ( sK4_SY18 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [SX0: a] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY7 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [SX0: a] :
( ~ ( sK3_SY13 @ SX0 )
| ( sK4_SY18 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: a] :
( ~ ( ( sK1_X @ SX0 )
| ( sK3_SY13 @ SX0 ) )
| ( sK2_SY7 @ SX0 )
| ( sK4_SY18 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: a] :
( ( ~ ( sK1_X @ SV1 )
| ( sK2_SY7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a] :
( ( ~ ( sK3_SY13 @ SV2 )
| ( sK4_SY18 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ( sK1_X @ sK5_SX0 )
| ( sK3_SY13 @ sK5_SX0 ) )
| ( sK2_SY7 @ sK5_SX0 )
| ( sK4_SY18 @ sK5_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV1: a] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $true )
| ( ( sK2_SY7 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a] :
( ( ( ~ ( sK3_SY13 @ SV2 ) )
= $true )
| ( ( sK4_SY18 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ( sK1_X @ sK5_SX0 )
| ( sK3_SY13 @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sK2_SY7 @ sK5_SX0 )
| ( sK4_SY18 @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: a] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( sK2_SY7 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: a] :
( ( ( sK3_SY13 @ SV2 )
= $false )
| ( ( sK4_SY18 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( sK1_X @ sK5_SX0 )
| ( sK3_SY13 @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( sK2_SY7 @ sK5_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( sK4_SY18 @ sK5_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ( sK1_X @ sK5_SX0 )
= $true )
| ( ( sK3_SY13 @ sK5_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,31,30,29,27]) ).
thf(33,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET200^5 : 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
% 0.09/0.15 % Computer : n002.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 14:38:12 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19
% 0.09/0.19 No.of.Axioms: 0
% 0.09/0.19
% 0.09/0.19 Length.of.Defs: 0
% 0.09/0.19
% 0.09/0.19 Contains.Choice.Funs: false
% 0.09/0.19
% 0.09/0.19 ********************************
% 0.09/0.19 * All subproblems solved! *
% 0.09/0.19 ********************************
% 0.09/0.19 % SZS status Theorem for /export/starexec/sandbox/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:32,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.19
% 0.09/0.19 %**** Beginning of derivation protocol ****
% 0.09/0.19 % SZS output start CNFRefutation
% See solution above
% 0.09/0.19
% 0.09/0.19 %**** End of derivation protocol ****
% 0.09/0.19 %**** no. of clauses in derivation: 33 ****
% 0.09/0.19 %**** clause counter: 32 ****
% 0.09/0.19
% 0.09/0.19 % SZS status Theorem for /export/starexec/sandbox/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:32,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------