%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV017^5 : 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 : n012.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 10:49:23 AM UTC 2026
% Result : Theorem 0.08s 0.12s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 42 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 51 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 368 ( 48 ~; 36 |; 14 &; 240 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xr,type,
sK1_Xr: a > a > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: a ).
thf(tp_sK3_SY22,type,
sK3_SY22: a ).
thf(tp_sK4_SY25,type,
sK4_SY25: a ).
thf(1,conjecture,
! [Xr: a > a > $o] :
( ( ! [Xx: a] : ( Xr @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xr @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xr @ Xx @ Xy )
& ( Xr @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xz ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( Xr @ Xx @ Xy )
=> ( ( Xr @ Xy @ Xz )
=> ( Xr @ Xx @ Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM514_pme) ).
thf(2,negated_conjecture,
( ( ! [Xr: a > a > $o] :
( ( ! [Xx: a] : ( Xr @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xr @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xr @ Xx @ Xy )
& ( Xr @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xz ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( Xr @ Xx @ Xy )
=> ( ( Xr @ Xy @ Xz )
=> ( Xr @ Xx @ Xz ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr: a > a > $o] :
( ( ! [Xx: a] : ( Xr @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xr @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xr @ Xx @ Xy )
& ( Xr @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xz ) ) )
=> ! [Xx: a,Xy: a,Xz: a] :
( ( Xr @ Xx @ Xy )
=> ( ( Xr @ Xy @ Xz )
=> ( Xr @ Xx @ Xz ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ! [SY10: a] : ( sK1_Xr @ SY10 @ SY10 )
& ! [SY11: a,SY12: a] :
( ( sK1_Xr @ SY11 @ SY12 )
=> ( sK1_Xr @ SY12 @ SY11 ) )
& ! [SY13: a,SY14: a,SY15: a] :
( ( ( sK1_Xr @ SY13 @ SY14 )
& ( sK1_Xr @ SY14 @ SY15 ) )
=> ( sK1_Xr @ SY13 @ SY15 ) ) )
=> ! [SY16: a,SY17: a,SY18: a] :
( ( sK1_Xr @ SY16 @ SY17 )
=> ( ( sK1_Xr @ SY17 @ SY18 )
=> ( sK1_Xr @ SY16 @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY10: a] : ( sK1_Xr @ SY10 @ SY10 ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY11: a,SY12: a] :
( ( sK1_Xr @ SY11 @ SY12 )
=> ( sK1_Xr @ SY12 @ SY11 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [SY13: a,SY14: a,SY15: a] :
( ( ( sK1_Xr @ SY13 @ SY14 )
& ( sK1_Xr @ SY14 @ SY15 ) )
=> ( sK1_Xr @ SY13 @ SY15 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [SY16: a,SY17: a,SY18: a] :
( ( sK1_Xr @ SY16 @ SY17 )
=> ( ( sK1_Xr @ SY17 @ SY18 )
=> ( sK1_Xr @ SY16 @ SY18 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(9,plain,
( ( ~ ! [SY16: a,SY17: a,SY18: a] :
( ( sK1_Xr @ SY16 @ SY17 )
=> ( ( sK1_Xr @ SY17 @ SY18 )
=> ( sK1_Xr @ SY16 @ SY18 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY13: a,SY14: a,SY15: a] :
( ( ( sK1_Xr @ SY13 @ SY14 )
& ( sK1_Xr @ SY14 @ SY15 ) )
=> ( sK1_Xr @ SY13 @ SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SY11: a,SY12: a] :
( ( sK1_Xr @ SY11 @ SY12 )
=> ( sK1_Xr @ SY12 @ SY11 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ! [SY10: a] : ( sK1_Xr @ SY10 @ SY10 ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ~ ! [SY16: a,SY17: a,SY18: a] :
( ( sK1_Xr @ SY16 @ SY17 )
=> ( ( sK1_Xr @ SY17 @ SY18 )
=> ( sK1_Xr @ SY16 @ SY18 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ ! [SX0: a,SX1: a,SX2: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 )
| ~ ( sK1_Xr @ SX1 @ SX2 )
| ( sK1_Xr @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 )
| ( sK1_Xr @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( sK1_Xr @ SX0 @ SX1 )
| ~ ( sK1_Xr @ SX1 @ SX2 ) )
| ( sK1_Xr @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(17,plain,
! [SV1: a] :
( ( sK1_Xr @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ( sK1_Xr @ SX0 @ SX1 )
| ~ ( sK1_Xr @ SX1 @ SX2 )
| ( sK1_Xr @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: a] :
( ( ! [SY19: a] :
( ~ ( sK1_Xr @ SV2 @ SY19 )
| ( sK1_Xr @ SY19 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: a] :
( ( ! [SY20: a,SY21: a] :
( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SY20 )
| ~ ( sK1_Xr @ SY20 @ SY21 ) )
| ( sK1_Xr @ SV3 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY22: a,SY23: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ SY22 )
| ~ ( sK1_Xr @ SY22 @ SY23 )
| ( sK1_Xr @ sK2_SX0 @ SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV4: a,SV2: a] :
( ( ~ ( sK1_Xr @ SV2 @ SV4 )
| ( sK1_Xr @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV5: a,SV3: a] :
( ( ! [SY24: a] :
( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SV5 )
| ~ ( sK1_Xr @ SV5 @ SY24 ) )
| ( sK1_Xr @ SV3 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SY25: a] :
( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY22 )
| ~ ( sK1_Xr @ sK3_SY22 @ SY25 )
| ( sK1_Xr @ sK2_SX0 @ SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(25,plain,
! [SV4: a,SV2: a] :
( ( ( ~ ( sK1_Xr @ SV2 @ SV4 ) )
= $true )
| ( ( sK1_Xr @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SV5 )
| ~ ( sK1_Xr @ SV5 @ SV6 ) )
| ( sK1_Xr @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY22 )
| ~ ( sK1_Xr @ sK3_SY22 @ sK4_SY25 )
| ( sK1_Xr @ sK2_SX0 @ sK4_SY25 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(28,plain,
! [SV4: a,SV2: a] :
( ( ( sK1_Xr @ SV2 @ SV4 )
= $false )
| ( ( sK1_Xr @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_Xr @ SV3 @ SV5 )
| ~ ( sK1_Xr @ SV5 @ SV6 ) ) )
= $true )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( sK1_Xr @ sK2_SX0 @ sK3_SY22 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( sK1_Xr @ sK3_SY22 @ sK4_SY25 )
| ( sK1_Xr @ sK2_SX0 @ sK4_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ( ~ ( ~ ( sK1_Xr @ SV3 @ SV5 )
| ~ ( sK1_Xr @ SV5 @ SV6 ) ) )
= $false )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( sK1_Xr @ sK2_SX0 @ sK3_SY22 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( sK1_Xr @ sK3_SY22 @ sK4_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( sK1_Xr @ sK2_SX0 @ sK4_SY25 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ( ~ ( sK1_Xr @ SV3 @ SV5 )
| ~ ( sK1_Xr @ SV5 @ SV6 ) )
= $true )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( sK1_Xr @ sK3_SY22 @ sK4_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ( ~ ( sK1_Xr @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( sK1_Xr @ SV5 @ SV6 ) )
= $true )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV6: a,SV5: a,SV3: a] :
( ( ( sK1_Xr @ SV3 @ SV5 )
= $false )
| ( ( ~ ( sK1_Xr @ SV5 @ SV6 ) )
= $true )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: a,SV6: a,SV5: a] :
( ( ( sK1_Xr @ SV5 @ SV6 )
= $false )
| ( ( sK1_Xr @ SV3 @ SV5 )
= $false )
| ( ( sK1_Xr @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,40,37,35,33,28]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV017^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:39:30 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.12
% 0.08/0.12 No.of.Axioms: 0
% 0.08/0.12
% 0.08/0.12 Length.of.Defs: 0
% 0.08/0.12
% 0.08/0.12 Contains.Choice.Funs: false
% 0.08/0.12 .
% 0.08/0.12
% 0.08/0.12 ********************************
% 0.08/0.12 * All subproblems solved! *
% 0.08/0.12 ********************************
% 0.08/0.12 % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.12
% 0.08/0.12 %**** Beginning of derivation protocol ****
% 0.08/0.12 % SZS output start CNFRefutation
% See solution above
% 0.08/0.12
% 0.08/0.12 %**** End of derivation protocol ****
% 0.08/0.12 %**** no. of clauses in derivation: 42 ****
% 0.08/0.12 %**** clause counter: 41 ****
% 0.08/0.12
% 0.08/0.12 % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------