%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV433^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n020.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 10:50:05 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 105 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 105 ( 19 ~; 45 |; 0 &; 38 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY5,type,
sK2_SY5: $i ).
thf(tp_sK3_SY7,type,
sK3_SY7: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( ( f @ X )
= ( f @ Y ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finj) ).
thf(2,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( X = Y )
| ( X = Z )
| ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less3) ).
thf(3,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( X = Y )
| ( X = Z )
| ( Y = Z ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( X = Y )
| ( X = Z )
| ( Y = Z ) ) )
= $false ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [X: $i,Y: $i] :
( ( ( f @ X )
= ( f @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(6,plain,
( ( ! [SY5: $i,SY6: $i] :
( ( sK1_X = SY5 )
| ( sK1_X = SY6 )
| ( SY5 = SY6 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(7,plain,
( ( ! [SY7: $i] :
( ( sK1_X = sK2_SY5 )
| ( sK1_X = SY7 )
| ( sK2_SY5 = SY7 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( sK1_X = sK2_SY5 )
| ( sK1_X = sK3_SY7 )
| ( sK2_SY5 = sK3_SY7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ~ ( ( sK1_X = sK2_SY5 )
| ( sK1_X = sK3_SY7 )
| ( sK2_SY5 = sK3_SY7 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( ( f @ X )
= ( f @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ~ ( ( sK1_X = sK2_SY5 )
| ( sK1_X = sK3_SY7 )
| ( sK2_SY5 = sK3_SY7 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( f @ SX0 )
!= ( f @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
( ( ( sK1_X = sK2_SY5 )
| ( sK1_X = sK3_SY7 )
| ( sK2_SY5 = sK3_SY7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
( ( ( f @ SV1 )
!= ( f @ SY8 ) )
| ( SV1 = SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ( sK1_X = sK2_SY5 )
| ( sK1_X = sK3_SY7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( sK2_SY5 = sK3_SY7 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( f @ SV1 )
!= ( f @ SV2 ) )
| ( SV1 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( sK1_X = sK2_SY5 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( sK1_X = sK3_SY7 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( f @ SV1 )
!= ( f @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( f @ SV1 )
= ( f @ SV2 ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( ( f @ SV1 )
| ( f @ SV2 ) )
| ~ ( ~ ( f @ SV1 )
| ~ ( f @ SV2 ) ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(23,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( f @ SV1 )
= ( f @ SV2 ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( ( f @ SV1 )
| ( f @ SV2 ) ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( f @ SV1 )
| ~ ( f @ SV2 ) ) )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV1: $i] :
( ( ( ( f @ SV1 )
| ( f @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( f @ SV1 )
| ~ ( f @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(28,plain,
! [SV2: $i,SV1: $i] :
( ( ( f @ SV1 )
= $true )
| ( ( f @ SV2 )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( f @ SV1 ) )
= $true )
| ( ( ~ ( f @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV2: $i,SV1: $i] :
( ( ( f @ SV1 )
= $false )
| ( ( ~ ( f @ SV2 ) )
= $true )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV1: $i,SV2: $i] :
( ( ( f @ SV2 )
= $false )
| ( ( f @ SV1 )
= $false )
| ( ( SV1 = SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(32,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,31,28,23,19,18]) ).
thf(33,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV433^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:47:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 1
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 0
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % 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:32,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 33 ****
% 0.07/0.24 %**** clause counter: 32 ****
% 0.07/0.24
% 0.07/0.24 % 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:32,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------