%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV434^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.11s 0.23s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 63 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 290 ( 156 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 147 ( 8 ~; 29 |; 0 &; 110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 32 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $o > $i ).
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(tp_sK4_SY8,type,
sK4_SY8: $i > $o ).
thf(1,axiom,
! [Y: $i] :
? [X: $o] :
( ( f @ X )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fsurj) ).
thf(2,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( X = Y )
| ( X = Z )
| ( Y = Z ) ),
file('/export/starexec/sandbox/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,
( ( ! [Y: $i] :
? [X: $o] :
( ( f @ 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,
( ( ! [Y: $i] :
? [X: $o] :
( ( f @ 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: $o] :
( ( f @ SX1 )
!= SX0 ) )
= $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: $o] :
( ( f @ SY8 )
!= SV1 ) )
= $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,
! [SV1: $i] :
( ( ! [SY8: $o] :
( ( f @ SY8 )
!= SV1 ) )
= $false ),
inference(extcnf_not_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,
! [SV1: $i] :
( ( ( f @ ( sK4_SY8 @ SV1 ) )
!= SV1 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( ( f @ ( sK4_SY8 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(22,plain,
! [SV2: $i] :
( ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 )
= $true ),
inference(rename,[status(thm)],[21]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 )
= ( sK1_X = sK3_SY7 ) )
= $false ),
inference(res,[status(thm)],[22,19]) ).
thf(24,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 )
= ( sK1_X = sK2_SY5 ) )
= $false ),
inference(res,[status(thm)],[22,18]) ).
thf(25,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 )
= ( sK2_SY5 = sK3_SY7 ) )
= $false ),
inference(res,[status(thm)],[22,16]) ).
thf(26,plain,
( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= sK3_SY7 )
= $false ),
inference(extuni,[status(esa)],[25:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(27,plain,
( ( ( f @ ( sK4_SY8 @ sK3_SY7 ) )
= sK2_SY5 )
= $false ),
inference(extuni,[status(esa)],[25:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(28,plain,
( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= sK2_SY5 )
= $false ),
inference(extuni,[status(esa)],[24:[bind(SV2,$thf( sK1_X ))]]) ).
thf(29,plain,
( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= sK1_X )
= $false ),
inference(extuni,[status(esa)],[24:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(30,plain,
( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= sK3_SY7 )
= $false ),
inference(extuni,[status(esa)],[23:[bind(SV2,$thf( sK1_X ))]]) ).
thf(31,plain,
( ( ( f @ ( sK4_SY8 @ sK3_SY7 ) )
= sK1_X )
= $false ),
inference(extuni,[status(esa)],[23:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= sK3_SY7 )
= ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 ) )
= $false ),
inference(res,[status(thm)],[26,22]) ).
thf(33,plain,
( ( sK3_SY7
= ( f @ ( sK4_SY8 @ ( f @ ( sK4_SY8 @ sK2_SY5 ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[32:[bind(SV2,$thf( f @ ( sK4_SY8 @ sK2_SY5 ) ))]]) ).
thf(34,plain,
( ( sK3_SY7 = sK2_SY5 )
= $false ),
inference(extuni,[status(esa)],[32:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(35,plain,
( ( ( sK4_SY8 @ sK2_SY5 )
= $true )
| ( ( sK4_SY8 @ sK3_SY7 )
= $true ) ),
inference(extuni,[status(esa)],[32:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(36,plain,
( ( ( sK4_SY8 @ sK2_SY5 )
= $false )
| ( ( sK4_SY8 @ sK3_SY7 )
= $false ) ),
inference(extuni,[status(esa)],[32:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(37,plain,
( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= ( f @ ( sK4_SY8 @ sK3_SY7 ) ) )
= $false ),
inference(extuni,[status(esa)],[32:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ sK3_SY7 ) )
= sK2_SY5 )
= ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 ) )
= $false ),
inference(res,[status(thm)],[27,22]) ).
thf(39,plain,
( ( sK2_SY5
= ( f @ ( sK4_SY8 @ ( f @ ( sK4_SY8 @ sK3_SY7 ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[38:[bind(SV2,$thf( f @ ( sK4_SY8 @ sK3_SY7 ) ))]]) ).
thf(40,plain,
( ( sK2_SY5 = sK3_SY7 )
= $false ),
inference(extuni,[status(esa)],[38:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(41,plain,
( ( ( sK4_SY8 @ sK3_SY7 )
= $true )
| ( ( sK4_SY8 @ sK2_SY5 )
= $true ) ),
inference(extuni,[status(esa)],[38:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(42,plain,
( ( ( sK4_SY8 @ sK3_SY7 )
= $false )
| ( ( sK4_SY8 @ sK2_SY5 )
= $false ) ),
inference(extuni,[status(esa)],[38:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(43,plain,
( ( ( f @ ( sK4_SY8 @ sK3_SY7 ) )
= ( f @ ( sK4_SY8 @ sK2_SY5 ) ) )
= $false ),
inference(extuni,[status(esa)],[38:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(44,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= sK2_SY5 )
= ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 ) )
= $false ),
inference(res,[status(thm)],[28,22]) ).
thf(45,plain,
( ( sK2_SY5
= ( f @ ( sK4_SY8 @ ( f @ ( sK4_SY8 @ sK1_X ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( f @ ( sK4_SY8 @ sK1_X ) ))]]) ).
thf(46,plain,
( ( sK2_SY5 = sK1_X )
= $false ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( sK1_X ))]]) ).
thf(47,plain,
( ( ( sK4_SY8 @ sK1_X )
= $true )
| ( ( sK4_SY8 @ sK2_SY5 )
= $true ) ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(48,plain,
( ( ( sK4_SY8 @ sK1_X )
= $false )
| ( ( sK4_SY8 @ sK2_SY5 )
= $false ) ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(49,plain,
( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= ( f @ ( sK4_SY8 @ sK2_SY5 ) ) )
= $false ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= sK1_X )
= ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 ) )
= $false ),
inference(res,[status(thm)],[29,22]) ).
thf(51,plain,
( ( sK1_X
= ( f @ ( sK4_SY8 @ ( f @ ( sK4_SY8 @ sK2_SY5 ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[50:[bind(SV2,$thf( f @ ( sK4_SY8 @ sK2_SY5 ) ))]]) ).
thf(52,plain,
( ( sK1_X = sK2_SY5 )
= $false ),
inference(extuni,[status(esa)],[50:[bind(SV2,$thf( sK2_SY5 ))]]) ).
thf(53,plain,
( ( ( sK4_SY8 @ sK2_SY5 )
= $true )
| ( ( sK4_SY8 @ sK1_X )
= $true ) ),
inference(extuni,[status(esa)],[50:[bind(SV2,$thf( sK1_X ))]]) ).
thf(54,plain,
( ( ( sK4_SY8 @ sK2_SY5 )
= $false )
| ( ( sK4_SY8 @ sK1_X )
= $false ) ),
inference(extuni,[status(esa)],[50:[bind(SV2,$thf( sK1_X ))]]) ).
thf(55,plain,
( ( ( f @ ( sK4_SY8 @ sK2_SY5 ) )
= ( f @ ( sK4_SY8 @ sK1_X ) ) )
= $false ),
inference(extuni,[status(esa)],[50:[bind(SV2,$thf( sK1_X ))]]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= sK3_SY7 )
= ( ( f @ ( sK4_SY8 @ SV2 ) )
= SV2 ) )
= $false ),
inference(res,[status(thm)],[30,22]) ).
thf(57,plain,
( ( sK3_SY7
= ( f @ ( sK4_SY8 @ ( f @ ( sK4_SY8 @ sK1_X ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( f @ ( sK4_SY8 @ sK1_X ) ))]]) ).
thf(58,plain,
( ( sK3_SY7 = sK1_X )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( sK1_X ))]]) ).
thf(59,plain,
( ( ( sK4_SY8 @ sK1_X )
= $true )
| ( ( sK4_SY8 @ sK3_SY7 )
= $true ) ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(60,plain,
( ( ( sK4_SY8 @ sK1_X )
= $false )
| ( ( sK4_SY8 @ sK3_SY7 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(61,plain,
( ( ( f @ ( sK4_SY8 @ sK1_X ) )
= ( f @ ( sK4_SY8 @ sK3_SY7 ) ) )
= $false ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( sK3_SY7 ))]]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,61,60,59,58,57,55,54,53,52,51,49,48,47,46,45,43,42,41,40,39,37,36,35,34,33,31,30,29,28,27,26,22,19,18]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV434^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n010.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 15:46:55 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.23
% 0.11/0.23 No.of.Axioms: 1
% 0.11/0.23
% 0.11/0.23 Length.of.Defs: 0
% 0.11/0.23
% 0.11/0.23 Contains.Choice.Funs: false
% 0.11/0.23 .
% 0.11/0.23
% 0.11/0.23 ********************************
% 0.11/0.23 * All subproblems solved! *
% 0.11/0.23 ********************************
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:10,foatp_calls:3,translation:fof_full)
% 0.11/0.23
% 0.11/0.23 %**** Beginning of derivation protocol ****
% 0.11/0.23 % SZS output start CNFRefutation
% See solution above
% 0.11/0.23
% 0.11/0.23 %**** End of derivation protocol ****
% 0.11/0.23 %**** no. of clauses in derivation: 63 ****
% 0.11/0.23 %**** clause counter: 62 ****
% 0.11/0.23
% 0.11/0.23 % SZS status Theorem for /export/starexec/sandbox/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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:62,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------