%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET631^5 : 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 : n016.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 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 165 ( 46 ~; 13 |; 26 &; 74 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 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 : 33 ( 0 ^; 18 !; 15 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY5,type,
sK2_SY5: a > $o ).
thf(tp_sK3_SY9,type,
sK3_SY9: a > $o ).
thf(tp_sK4_SY12,type,
sK4_SY12: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o,Z: a > $o] :
( ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx )
& ~ ( Z @ Xx ) )
=> ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_113_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx )
& ~ ( Z @ Xx ) )
=> ? [Xx: a] :
( ( 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] :
( ( X @ Xx )
& ( Y @ Xx )
& ~ ( Z @ Xx ) )
=> ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: a > $o,SY6: a > $o] :
( ? [SY7: a] :
( ( sK1_X @ SY7 )
& ( SY5 @ SY7 )
& ~ ( SY6 @ SY7 ) )
=> ? [SY8: a] :
( ( sK1_X @ SY8 )
& ( SY5 @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY9: a > $o] :
( ? [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 )
& ~ ( SY9 @ SY10 ) )
=> ? [SY11: a] :
( ( sK1_X @ SY11 )
& ( sK2_SY5 @ SY11 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ? [SY12: a] :
( ( sK1_X @ SY12 )
& ( sK2_SY5 @ SY12 )
& ~ ( sK3_SY9 @ SY12 ) )
=> ? [SY11: a] :
( ( sK1_X @ SY11 )
& ( sK2_SY5 @ SY11 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ? [SY12: a] :
( ( sK1_X @ SY12 )
& ( sK2_SY5 @ SY12 )
& ~ ( sK3_SY9 @ SY12 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ? [SY11: a] :
( ( sK1_X @ SY11 )
& ( sK2_SY5 @ SY11 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ? [SY11: a] :
( ( sK1_X @ SY11 )
& ( sK2_SY5 @ SY11 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY11: a] :
( ~ ( sK1_X @ SY11 )
| ~ ( sK2_SY5 @ SY11 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ( sK1_X @ sK4_SY12 )
& ( sK2_SY5 @ sK4_SY12 )
& ~ ( sK3_SY9 @ sK4_SY12 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(12,plain,
( ( ( sK1_X @ sK4_SY12 )
& ( sK2_SY5 @ sK4_SY12 )
& ~ ( sK3_SY9 @ sK4_SY12 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY11: a] :
( ~ ( sK1_X @ SY11 )
| ~ ( sK2_SY5 @ SY11 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( ~ ~ ( ~ ( sK1_X @ sK4_SY12 )
| ~ ( sK2_SY5 @ sK4_SY12 ) )
| ~ ~ ( sK3_SY9 @ sK4_SY12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: a] :
( ( ~ ( sK1_X @ SV1 )
| ~ ( sK2_SY5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ( sK1_X @ sK4_SY12 )
| ~ ( sK2_SY5 @ sK4_SY12 ) )
| ~ ~ ( sK3_SY9 @ sK4_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV1: a] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $true )
| ( ( ~ ( sK2_SY5 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( sK1_X @ sK4_SY12 )
| ~ ( sK2_SY5 @ sK4_SY12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( sK3_SY9 @ sK4_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: a] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( ~ ( sK2_SY5 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( ~ ( sK1_X @ sK4_SY12 )
| ~ ( sK2_SY5 @ sK4_SY12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( sK3_SY9 @ sK4_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: a] :
( ( ( sK2_SY5 @ SV1 )
= $false )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( sK1_X @ sK4_SY12 )
| ~ ( sK2_SY5 @ sK4_SY12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( sK3_SY9 @ sK4_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK1_X @ sK4_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( sK2_SY5 @ sK4_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( sK1_X @ sK4_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( sK2_SY5 @ sK4_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,29,28,25]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET631^5 : 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
% 0.08/0.20 % Computer : n016.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 14:52:44 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:30,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 31 ****
% 0.08/0.23 %**** clause counter: 30 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:30,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------