%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN375^5 : 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 11:05:40 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 51 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 221 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 185 ( 41 ~; 22 |; 7 &; 96 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 53 !; 16 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_Xy,type,
sK2_Xy: $i ).
thf(tp_sK3_Xy,type,
sK3_Xy: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i ).
thf(1,conjecture,
( ( ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) )
& ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) ) )
=> ( ? [Xy: $i] : ( cP @ Xy )
<=> ! [Xx: $i] : ( cP @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2126_BUG) ).
thf(2,negated_conjecture,
( ( ( ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) )
& ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) ) )
=> ( ? [Xy: $i] : ( cP @ Xy )
<=> ! [Xx: $i] : ( cP @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) )
& ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) ) )
=> ( ? [Xy: $i] : ( cP @ Xy )
<=> ! [Xx: $i] : ( cP @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [Xy: $i] : ( cP @ Xy )
<=> ! [Xx: $i] : ( cP @ Xx ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(8,plain,
( ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[6]) ).
thf(9,plain,
( ( ~ ( ? [Xy: $i] : ( cP @ Xy )
=> ! [Xx: $i] : ( cP @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ! [Xx: $i] : ( cP @ Xx )
=> ? [Xy: $i] : ( cP @ Xy ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ( cP @ sK2_Xy )
& ~ ( cP @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [Xx: $i] : ( cP @ Xx )
& ! [Xy: $i] :
~ ( cP @ Xy ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ~ ( cP @ sK4_Xx )
| ( cP @ sK3_Xy ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(14,plain,
( ( ! [Xy: $i] :
~ ( cP @ Xy )
| ! [Xx: $i] : ( cP @ Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(15,plain,
( ( ! [Xy: $i] :
~ ( cP @ Xy )
| ! [Xx: $i] : ( cP @ Xx ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( cP @ sK4_Xx )
| ( cP @ sK3_Xy ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ( cP @ sK2_Xy )
& ~ ( cP @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ~ ( ~ ( cP @ sK2_Xy )
| ~ ~ ( cP @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ( ! [Xy: $i] :
~ ( cP @ Xy ) )
= $true )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ( ~ ( cP @ sK4_Xx ) )
= $true )
| ( ( cP @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( cP @ sK2_Xy )
| ~ ~ ( cP @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( ~ ( cP @ SV1 ) )
= $true )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ( cP @ sK4_Xx )
= $false )
| ( ( cP @ sK3_Xy )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( cP @ sK2_Xy ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ~ ( cP @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( cP @ SV1 )
= $false )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( cP @ sK2_Xy )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( cP @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i,SV2: $i] :
( ( ( cP @ SV2 )
= $true )
| ( ( cP @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( cP @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,30,29,27]) ).
thf(32,plain,
( ( ! [Xy: $i] :
~ ( cP @ Xy )
| ! [Xx: $i] : ( cP @ Xx ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(33,plain,
( ( ~ ( cP @ sK4_Xx )
| ( cP @ sK3_Xy ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(34,plain,
( ( ! [Xx: $i] : ( cP @ Xx )
& ! [Xy: $i] :
~ ( cP @ Xy ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(35,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP @ SX0 )
| ~ ! [SX0: $i] :
~ ( cP @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ( ! [Xy: $i] :
~ ( cP @ Xy ) )
= $true )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( ( ~ ( cP @ sK4_Xx ) )
= $true )
| ( ( cP @ sK3_Xy )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ! [SX0: $i] : ( cP @ SX0 )
| ~ ! [SX0: $i] :
~ ( cP @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV3: $i] :
( ( ( ~ ( cP @ SV3 ) )
= $true )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
( ( ( cP @ sK4_Xx )
= $false )
| ( ( cP @ sK3_Xy )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( ~ ! [SX0: $i] : ( cP @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ~ ! [SX0: $i] :
~ ( cP @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: $i] :
( ( ( cP @ SV3 )
= $false )
| ( ( ! [Xx: $i] : ( cP @ Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ! [SX0: $i] : ( cP @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ! [SX0: $i] :
~ ( cP @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV4: $i] :
( ( ( cP @ SV4 )
= $true )
| ( ( cP @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV5: $i] :
( ( cP @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV6: $i] :
( ( ~ ( cP @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV6: $i] :
( ( cP @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,49,47,46]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN375^5 : 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
% 0.10/0.21 % Computer : n004.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Oct 6 17:19:24 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.27
% 0.10/0.27 No.of.Axioms: 0
% 0.10/0.27
% 0.10/0.27 Length.of.Defs: 0
% 0.10/0.27
% 0.10/0.27 Contains.Choice.Funs: false
% 0.10/0.27
% 0.10/0.27 ********************************
% 0.10/0.27 * All subproblems solved! *
% 0.10/0.27 ********************************
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/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:50,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.10/0.27
% 0.10/0.27 %**** Beginning of derivation protocol ****
% 0.10/0.27 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27
% 0.10/0.27 %**** End of derivation protocol ****
% 0.10/0.27 %**** no. of clauses in derivation: 51 ****
% 0.10/0.27 %**** clause counter: 50 ****
% 0.10/0.27
% 0.10/0.27 % SZS status Theorem for /export/starexec/sandbox2/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:50,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------