%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV061^5 : 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 10:49:28 AM UTC 2026
% Result : Theorem 0.07s 0.12s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 42 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 252 ( 141 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 376 ( 110 ~; 63 |; 29 &; 148 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 83 ( 0 ^; 83 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_sK1_Xx,type,
sK1_Xx: b ).
thf(tp_sK2_SY8,type,
sK2_SY8: a ).
thf(tp_sK3_SY15,type,
sK3_SY15: b > a > $o ).
thf(tp_sK4_SY21,type,
sK4_SY21: b > a > $o ).
thf(tp_sK5_SX0,type,
sK5_SX0: b ).
thf(tp_sK6_SY31,type,
sK6_SY31: a ).
thf(1,conjecture,
! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
( ! [Xx_2: b,Xy_47: a] :
( ( Xk @ Xx_2 @ Xy_47 )
=> ( ( Xs @ Xx_2 @ Xy_47 )
| ( ( Xx_2 = Xx )
& ( Xy_47 = Xy ) ) ) )
=> ! [Xx_3: b,Xy_48: a] :
( ( ( Xk @ Xx_3 @ Xy_48 )
& ~ ( ( Xx_3 = Xx )
& ( Xy_48 = Xy ) ) )
=> ( Xs @ Xx_3 @ Xy_48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM176_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
( ! [Xx_2: b,Xy_47: a] :
( ( Xk @ Xx_2 @ Xy_47 )
=> ( ( Xs @ Xx_2 @ Xy_47 )
| ( ( Xx_2 = Xx )
& ( Xy_47 = Xy ) ) ) )
=> ! [Xx_3: b,Xy_48: a] :
( ( ( Xk @ Xx_3 @ Xy_48 )
& ~ ( ( Xx_3 = Xx )
& ( Xy_48 = Xy ) ) )
=> ( Xs @ Xx_3 @ Xy_48 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
( ! [Xx_2: b,Xy_47: a] :
( ( Xk @ Xx_2 @ Xy_47 )
=> ( ( Xs @ Xx_2 @ Xy_47 )
| ( ( Xx_2 = Xx )
& ( Xy_47 = Xy ) ) ) )
=> ! [Xx_3: b,Xy_48: a] :
( ( ( Xk @ Xx_3 @ Xy_48 )
& ~ ( ( Xx_3 = Xx )
& ( Xy_48 = Xy ) ) )
=> ( Xs @ Xx_3 @ Xy_48 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY8: a,SY9: b > a > $o,SY10: b > a > $o] :
( ! [SY11: b,SY12: a] :
( ( SY10 @ SY11 @ SY12 )
=> ( ( SY9 @ SY11 @ SY12 )
| ( ( SY11 = sK1_Xx )
& ( SY12 = SY8 ) ) ) )
=> ! [SY13: b,SY14: a] :
( ( ( SY10 @ SY13 @ SY14 )
& ~ ( ( SY13 = sK1_Xx )
& ( SY14 = SY8 ) ) )
=> ( SY9 @ SY13 @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY15: b > a > $o,SY16: b > a > $o] :
( ! [SY17: b,SY18: a] :
( ( SY16 @ SY17 @ SY18 )
=> ( ( SY15 @ SY17 @ SY18 )
| ( ( SY17 = sK1_Xx )
& ( SY18 = sK2_SY8 ) ) ) )
=> ! [SY19: b,SY20: a] :
( ( ( SY16 @ SY19 @ SY20 )
& ~ ( ( SY19 = sK1_Xx )
& ( SY20 = sK2_SY8 ) ) )
=> ( SY15 @ SY19 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY21: b > a > $o] :
( ! [SY22: b,SY23: a] :
( ( SY21 @ SY22 @ SY23 )
=> ( ( sK3_SY15 @ SY22 @ SY23 )
| ( ( SY22 = sK1_Xx )
& ( SY23 = sK2_SY8 ) ) ) )
=> ! [SY24: b,SY25: a] :
( ( ( SY21 @ SY24 @ SY25 )
& ~ ( ( SY24 = sK1_Xx )
& ( SY25 = sK2_SY8 ) ) )
=> ( sK3_SY15 @ SY24 @ SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY26: b,SY27: a] :
( ( sK4_SY21 @ SY26 @ SY27 )
=> ( ( sK3_SY15 @ SY26 @ SY27 )
| ( ( SY26 = sK1_Xx )
& ( SY27 = sK2_SY8 ) ) ) )
=> ! [SY28: b,SY29: a] :
( ( ( sK4_SY21 @ SY28 @ SY29 )
& ~ ( ( SY28 = sK1_Xx )
& ( SY29 = sK2_SY8 ) ) )
=> ( sK3_SY15 @ SY28 @ SY29 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY26: b,SY27: a] :
( ( sK4_SY21 @ SY26 @ SY27 )
=> ( ( sK3_SY15 @ SY26 @ SY27 )
| ( ( SY26 = sK1_Xx )
& ( SY27 = sK2_SY8 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY28: b,SY29: a] :
( ( ( sK4_SY21 @ SY28 @ SY29 )
& ~ ( ( SY28 = sK1_Xx )
& ( SY29 = sK2_SY8 ) ) )
=> ( sK3_SY15 @ SY28 @ SY29 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SY28: b,SY29: a] :
( ( ( sK4_SY21 @ SY28 @ SY29 )
& ~ ( ( SY28 = sK1_Xx )
& ( SY29 = sK2_SY8 ) ) )
=> ( sK3_SY15 @ SY28 @ SY29 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY26: b,SY27: a] :
( ( sK4_SY21 @ SY26 @ SY27 )
=> ( ( sK3_SY15 @ SY26 @ SY27 )
| ( ( SY26 = sK1_Xx )
& ( SY27 = sK2_SY8 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SY28: b,SY29: a] :
( ( ( sK4_SY21 @ SY28 @ SY29 )
& ~ ( ( SY28 = sK1_Xx )
& ( SY29 = sK2_SY8 ) ) )
=> ( sK3_SY15 @ SY28 @ SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: b,SX1: a] :
( ~ ~ ( ~ ( sK4_SY21 @ SX0 @ SX1 )
| ~ ~ ~ ( ( SX0 != sK1_Xx )
| ( SX1 != sK2_SY8 ) ) )
| ( sK3_SY15 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SX0: b,SX1: a] :
( ~ ( sK4_SY21 @ SX0 @ SX1 )
| ( sK3_SY15 @ SX0 @ SX1 )
| ~ ( ( SX0 != sK1_Xx )
| ( SX1 != sK2_SY8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: b,SX1: a] :
( ~ ~ ( ~ ( sK4_SY21 @ SX0 @ SX1 )
| ~ ~ ~ ( ( SX0 != sK1_Xx )
| ( SX1 != sK2_SY8 ) ) )
| ( sK3_SY15 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: b] :
( ( ! [SY30: a] :
( ~ ( sK4_SY21 @ SV1 @ SY30 )
| ( sK3_SY15 @ SV1 @ SY30 )
| ~ ( ( SV1 != sK1_Xx )
| ( SY30 != sK2_SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SY31: a] :
( ~ ~ ( ~ ( sK4_SY21 @ sK5_SX0 @ SY31 )
| ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( SY31 != sK2_SY8 ) ) )
| ( sK3_SY15 @ sK5_SX0 @ SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: a,SV1: b] :
( ( ~ ( sK4_SY21 @ SV1 @ SV2 )
| ( sK3_SY15 @ SV1 @ SV2 )
| ~ ( ( SV1 != sK1_Xx )
| ( SV2 != sK2_SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( ~ ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 )
| ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) )
| ( sK3_SY15 @ sK5_SX0 @ sK6_SY31 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(20,plain,
! [SV2: a,SV1: b] :
( ( ( ~ ( sK4_SY21 @ SV1 @ SV2 ) )
= $true )
| ( ( ( sK3_SY15 @ SV1 @ SV2 )
| ~ ( ( SV1 != sK1_Xx )
| ( SV2 != sK2_SY8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 )
| ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( sK3_SY15 @ sK5_SX0 @ sK6_SY31 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a,SV1: b] :
( ( ( sK4_SY21 @ SV1 @ SV2 )
= $false )
| ( ( ( sK3_SY15 @ SV1 @ SV2 )
| ~ ( ( SV1 != sK1_Xx )
| ( SV2 != sK2_SY8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 )
| ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: a,SV1: b] :
( ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( ~ ( ( SV1 != sK1_Xx )
| ( SV2 != sK2_SY8 ) ) )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 )
| ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: a,SV1: b] :
( ( ( ( SV1 != sK1_Xx )
| ( SV2 != sK2_SY8 ) )
= $false )
| ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: a,SV1: b] :
( ( ( SV1 != sK1_Xx )
= $false )
| ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: b,SV2: a] :
( ( ( SV2 != sK2_SY8 )
= $false )
| ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( sK4_SY21 @ sK5_SX0 @ sK6_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: a,SV1: b] :
( ( ( SV1 = sK1_Xx )
= $true )
| ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: b,SV2: a] :
( ( ( SV2 = sK2_SY8 )
= $true )
| ( ( sK3_SY15 @ SV1 @ SV2 )
= $true )
| ( ( sK4_SY21 @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
( ( ( sK5_SX0 != sK1_Xx )
| ( sK6_SY31 != sK2_SY8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(38,plain,
( ( ( sK5_SX0 != sK1_Xx )
= $true )
| ( ( sK6_SY31 != sK2_SY8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(39,plain,
( ( ( sK5_SX0 = sK1_Xx )
= $false )
| ( ( sK6_SY31 != sK2_SY8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
( ( ( sK6_SY31 = sK2_SY8 )
= $false )
| ( ( sK5_SX0 = sK1_Xx )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,40,35,34,32]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV061^5 : 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 15:39:46 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
% 0.07/0.12
% 0.07/0.12 No.of.Axioms: 0
% 0.07/0.12
% 0.07/0.12 Length.of.Defs: 0
% 0.07/0.12
% 0.07/0.12 Contains.Choice.Funs: false
% 0.07/0.12 .
% 0.07/0.12
% 0.07/0.12 ********************************
% 0.07/0.12 * All subproblems solved! *
% 0.07/0.12 ********************************
% 0.07/0.12 % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.12
% 0.07/0.12 %**** Beginning of derivation protocol ****
% 0.07/0.12 % SZS output start CNFRefutation
% See solution above
% 0.07/0.12
% 0.07/0.12 %**** End of derivation protocol ****
% 0.07/0.12 %**** no. of clauses in derivation: 42 ****
% 0.07/0.12 %**** clause counter: 41 ****
% 0.07/0.12
% 0.07/0.12 % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------