%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV230^5 : 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 : n001.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 10:49:47 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 36 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 261 ( 41 ~; 41 |; 0 &; 127 @)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 ^; 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_U,type,
sK1_U: a > $o ).
thf(tp_sK2_SY8,type,
sK2_SY8: a > $o ).
thf(tp_sK3_SX0,type,
sK3_SX0: ( a > $o ) > $o ).
thf(tp_sK4_SY23,type,
sK4_SY23: a > $o ).
thf(tp_sK5_SY25,type,
sK5_SY25: a ).
thf(1,conjecture,
! [U: a > $o,V: a > $o] :
( ! [Xx: a] :
( ( U @ Xx )
=> ( V @ Xx ) )
=> ! [Xx: ( a > $o ) > $o] :
( ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( U @ Xx1 ) ) )
=> ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( V @ Xx1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM88_pme) ).
thf(2,negated_conjecture,
( ( ! [U: a > $o,V: a > $o] :
( ! [Xx: a] :
( ( U @ Xx )
=> ( V @ Xx ) )
=> ! [Xx: ( a > $o ) > $o] :
( ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( U @ Xx1 ) ) )
=> ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( V @ Xx1 ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [U: a > $o,V: a > $o] :
( ! [Xx: a] :
( ( U @ Xx )
=> ( V @ Xx ) )
=> ! [Xx: ( a > $o ) > $o] :
( ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( U @ Xx1 ) ) )
=> ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( V @ Xx1 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY8: a > $o] :
( ! [SY9: a] :
( ( sK1_U @ SY9 )
=> ( SY8 @ SY9 ) )
=> ! [SY10: ( a > $o ) > $o] :
( ! [SY11: a > $o] :
( ( SY10 @ SY11 )
=> ! [SY12: a] :
( ( SY11 @ SY12 )
=> ( sK1_U @ SY12 ) ) )
=> ! [Xx0: a > $o] :
( ( SY10 @ Xx0 )
=> ! [Xx1: a] :
( ( Xx0 @ Xx1 )
=> ( SY8 @ Xx1 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY15: a] :
( ( sK1_U @ SY15 )
=> ( sK2_SY8 @ SY15 ) )
=> ! [SY16: ( a > $o ) > $o] :
( ! [SY11: a > $o] :
( ( SY16 @ SY11 )
=> ! [SY12: a] :
( ( SY11 @ SY12 )
=> ( sK1_U @ SY12 ) ) )
=> ! [SY19: a > $o] :
( ( SY16 @ SY19 )
=> ! [SY20: a] :
( ( SY19 @ SY20 )
=> ( sK2_SY8 @ SY20 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY15: a] :
( ( sK1_U @ SY15 )
=> ( sK2_SY8 @ SY15 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY16: ( a > $o ) > $o] :
( ! [SY11: a > $o] :
( ( SY16 @ SY11 )
=> ! [SY12: a] :
( ( SY11 @ SY12 )
=> ( sK1_U @ SY12 ) ) )
=> ! [SY19: a > $o] :
( ( SY16 @ SY19 )
=> ! [SY20: a] :
( ( SY19 @ SY20 )
=> ( sK2_SY8 @ SY20 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY16: ( a > $o ) > $o] :
( ! [SY11: a > $o] :
( ( SY16 @ SY11 )
=> ! [SY12: a] :
( ( SY11 @ SY12 )
=> ( sK1_U @ SY12 ) ) )
=> ! [SY19: a > $o] :
( ( SY16 @ SY19 )
=> ! [SY20: a] :
( ( SY19 @ SY20 )
=> ( sK2_SY8 @ SY20 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY15: a] :
( ( sK1_U @ SY15 )
=> ( sK2_SY8 @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY16: ( a > $o ) > $o] :
( ! [SY11: a > $o] :
( ( SY16 @ SY11 )
=> ! [SY12: a] :
( ( SY11 @ SY12 )
=> ( sK1_U @ SY12 ) ) )
=> ! [SY19: a > $o] :
( ( SY16 @ SY19 )
=> ! [SY20: a] :
( ( SY19 @ SY20 )
=> ( sK2_SY8 @ SY20 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: a] :
( ~ ( sK1_U @ SX0 )
| ( sK2_SY8 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ! [SX0: ( a > $o ) > $o] :
( ~ ! [SX1: a > $o] :
( ~ ( SX0 @ SX1 )
| ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( sK1_U @ SX2 ) ) )
| ! [SX1: a > $o] :
( ~ ( SX0 @ SX1 )
| ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( sK2_SY8 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: a] :
( ( ~ ( sK1_U @ SV1 )
| ( sK2_SY8 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ! [SX1: a > $o] :
( ~ ( SX0 @ SX1 )
| ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( sK1_U @ SX2 ) ) )
| ! [SX1: a > $o] :
( ~ ( SX0 @ SX1 )
| ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( sK2_SY8 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: a] :
( ( ( ~ ( sK1_U @ SV1 ) )
= $true )
| ( ( sK2_SY8 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY21: a > $o] :
( ~ ( sK3_SX0 @ SY21 )
| ! [SX2: a] :
( ~ ( SY21 @ SX2 )
| ( sK1_U @ SX2 ) ) )
| ! [SY23: a > $o] :
( ~ ( sK3_SX0 @ SY23 )
| ! [SX2: a] :
( ~ ( SY23 @ SX2 )
| ( sK2_SY8 @ SX2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV1: a] :
( ( ( sK1_U @ SV1 )
= $false )
| ( ( sK2_SY8 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ! [SY21: a > $o] :
( ~ ( sK3_SX0 @ SY21 )
| ! [SX2: a] :
( ~ ( SY21 @ SX2 )
| ( sK1_U @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY23: a > $o] :
( ~ ( sK3_SX0 @ SY23 )
| ! [SX2: a] :
( ~ ( SY23 @ SX2 )
| ( sK2_SY8 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SY21: a > $o] :
( ~ ( sK3_SX0 @ SY21 )
| ! [SX2: a] :
( ~ ( SY21 @ SX2 )
| ( sK1_U @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( sK3_SX0 @ sK4_SY23 )
| ! [SY25: a] :
( ~ ( sK4_SY23 @ SY25 )
| ( sK2_SY8 @ SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(22,plain,
! [SV2: a > $o] :
( ( ~ ( sK3_SX0 @ SV2 )
| ! [SY26: a] :
( ~ ( SV2 @ SY26 )
| ( sK1_U @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( sK3_SX0 @ sK4_SY23 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [SY25: a] :
( ~ ( sK4_SY23 @ SY25 )
| ( sK2_SY8 @ SY25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: a > $o] :
( ( ( ~ ( sK3_SX0 @ SV2 ) )
= $true )
| ( ( ! [SY26: a] :
( ~ ( SV2 @ SY26 )
| ( sK1_U @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( sK3_SX0 @ sK4_SY23 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( sK4_SY23 @ sK5_SY25 )
| ( sK2_SY8 @ sK5_SY25 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(28,plain,
! [SV2: a > $o] :
( ( ( sK3_SX0 @ SV2 )
= $false )
| ( ( ! [SY26: a] :
( ~ ( SV2 @ SY26 )
| ( sK1_U @ SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( sK4_SY23 @ sK5_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
( ( sK2_SY8 @ sK5_SY25 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV3 )
| ( sK1_U @ SV3 ) )
= $true )
| ( ( sK3_SX0 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( sK4_SY23 @ sK5_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV3 ) )
= $true )
| ( ( sK1_U @ SV3 )
= $true )
| ( ( sK3_SX0 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ SV3 )
= $false )
| ( ( sK1_U @ SV3 )
= $true )
| ( ( sK3_SX0 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,34,32,30,26]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV230^5 : 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
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:49:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 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 ********************************
% 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:1,axioms:1,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 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: 36 ****
% 0.08/0.23 %**** clause counter: 35 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------