%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET632^5 : 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 : n007.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 10:40:40 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 48 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 233 ( 71 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 221 ( 56 ~; 28 |; 20 &; 95 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 65 ( 11 ^; 46 !; 8 ?; 65 :)
% 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_SV3,type,
sK4_SV3: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( X @ Xx )
=> ( Z @ Xx ) )
& ~ ? [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) )
=> ( X
= ( ^ [Xx: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_114_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( X @ Xx )
=> ( Z @ Xx ) )
& ~ ? [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) )
=> ( X
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( X @ Xx )
=> ( Z @ Xx ) )
& ~ ? [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) )
=> ( X
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY7: a > $o,SY8: a > $o] :
( ( ! [SY9: a] :
( ( sK1_X @ SY9 )
=> ( SY7 @ SY9 ) )
& ! [SY10: a] :
( ( sK1_X @ SY10 )
=> ( SY8 @ SY10 ) )
& ~ ? [Xx: a] :
( ( SY7 @ Xx )
& ( SY8 @ Xx ) ) )
=> ( sK1_X
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: a > $o] :
( ( ! [SY14: a] :
( ( sK1_X @ SY14 )
=> ( sK2_SY7 @ SY14 ) )
& ! [SY10: a] :
( ( sK1_X @ SY10 )
=> ( SY13 @ SY10 ) )
& ~ ? [SY16: a] :
( ( sK2_SY7 @ SY16 )
& ( SY13 @ SY16 ) ) )
=> ( sK1_X
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY14: a] :
( ( sK1_X @ SY14 )
=> ( sK2_SY7 @ SY14 ) )
& ! [SY19: a] :
( ( sK1_X @ SY19 )
=> ( sK3_SY13 @ SY19 ) )
& ~ ? [SY20: a] :
( ( sK2_SY7 @ SY20 )
& ( sK3_SY13 @ SY20 ) ) )
=> ( sK1_X
= ( ^ [Xx: a] : $false ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY14: a] :
( ( sK1_X @ SY14 )
=> ( sK2_SY7 @ SY14 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY19: a] :
( ( sK1_X @ SY19 )
=> ( sK3_SY13 @ SY19 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ? [SY20: a] :
( ( sK2_SY7 @ SY20 )
& ( sK3_SY13 @ SY20 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( sK1_X
= ( ^ [Xx: a] : $false ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(11,plain,
( ( sK1_X
!= ( ^ [Xx: a] : $false ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ? [SY20: a] :
( ( sK2_SY7 @ SY20 )
& ( sK3_SY13 @ SY20 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SY19: a] :
( ( sK1_X @ SY19 )
=> ( sK3_SY13 @ SY19 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [SY14: a] :
( ( sK1_X @ SY14 )
=> ( sK2_SY7 @ SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( sK1_X
!= ( ^ [Xx: a] : $false ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SX0: a] :
( ~ ( sK1_X @ SX0 )
| ( sK2_SY7 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: a] :
( ~ ( sK1_X @ SX0 )
| ( sK3_SY13 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK2_SY7 @ SX0 )
| ~ ( sK3_SY13 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(19,plain,
( ( sK1_X
= ( ^ [Xx: a] : $false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: a] :
( ( ~ ( sK1_X @ SV1 )
| ( sK2_SY7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: a] :
( ( ~ ( sK1_X @ SV2 )
| ( sK3_SY13 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ! [SX0: a] :
~ ~ ( ~ ( sK2_SY7 @ SX0 )
| ~ ( sK3_SY13 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SV3: a] :
( ( sK1_X @ SV3 )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( sK1_X
= ( ^ [Xx: a] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[19]) ).
thf(25,plain,
! [SV1: a] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $true )
| ( ( sK2_SY7 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV2: a] :
( ( ( ~ ( sK1_X @ SV2 ) )
= $true )
| ( ( sK3_SY13 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [SX0: a] :
~ ~ ( ~ ( sK2_SY7 @ SX0 )
| ~ ( sK3_SY13 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ( sK1_X @ sK4_SV3 )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(29,plain,
! [SV1: a] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( sK2_SY7 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $false )
| ( ( sK3_SY13 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: a] :
( ( ~ ~ ( ~ ( sK2_SY7 @ SV4 )
| ~ ( sK3_SY13 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( ( sK1_X @ sK4_SV3 )
| $false )
| ~ ( ~ ( sK1_X @ sK4_SV3 )
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ( sK1_X @ sK4_SV3 )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV4: a] :
( ( ~ ( ~ ( sK2_SY7 @ SV4 )
| ~ ( sK3_SY13 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ( ( sK1_X @ sK4_SV3 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ~ ( ~ ( sK1_X @ sK4_SV3 )
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: a] :
( ( ~ ( sK2_SY7 @ SV4 )
| ~ ( sK3_SY13 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
( ( ( sK1_X @ sK4_SV3 )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ( sK1_X @ sK4_SV3 )
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY7 @ SV4 ) )
= $true )
| ( ( ~ ( sK3_SY13 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( ( sK1_X @ sK4_SV3 )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
( ( ( ~ ( sK1_X @ sK4_SV3 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV4: a] :
( ( ( sK2_SY7 @ SV4 )
= $false )
| ( ( ~ ( sK3_SY13 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
( ( ( sK1_X @ sK4_SV3 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV4: a] :
( ( ( sK3_SY13 @ SV4 )
= $false )
| ( ( sK2_SY7 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
( ( $false = $false )
| ( ( sK1_X @ sK4_SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,46,45,41,33,30,29]) ).
thf(48,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632^5 : 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
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 14:45:45 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 0
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 48 ****
% 0.09/0.21 %**** clause counter: 47 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------