%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM647^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n007.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 10:34:46 AM UTC 2026
% Result : Theorem 0.10s 0.19s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 83 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 148 ( 62 ~; 24 |; 0 &; 56 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(tp_z,type,
z: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( Xy != Xz )
=> ( ( pl @ Xx @ Xy )
!= ( pl @ Xx @ Xz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8) ).
thf(2,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',et) ).
thf(3,axiom,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i) ).
thf(4,conjecture,
y = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8a) ).
thf(5,negated_conjecture,
( ( y = z )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( y = z )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( Xy != Xz )
=> ( ( pl @ Xx @ Xy )
!= ( pl @ Xx @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ( pl @ x @ y )
= ( pl @ x @ z ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( y != z )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(11,plain,
( ( ( pl @ x @ y )
= ( pl @ x @ z ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( Xy != Xz )
=> ( ( pl @ Xx @ Xy )
!= ( pl @ Xx @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( y != z )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ( SX1 != SX2 ) )
| ( ( pl @ SX0 @ SX1 )
!= ( pl @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SX0: $o] :
( ~ ~ ~ SX0
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(17,plain,
( ( y = z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: nat] :
( ( ! [SY4: nat,SY5: nat] :
( ~ ( ( SY4 != SY5 ) )
| ( ( pl @ SV1 @ SY4 )
!= ( pl @ SV1 @ SY5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $o] :
( ( ~ ~ ~ SV2
| SV2 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ~ ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV1: nat,SV3: nat] :
( ( ! [SY6: nat] :
( ~ ( ( SV3 != SY6 ) )
| ( ( pl @ SV1 @ SV3 )
!= ( pl @ SV1 @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $o] :
( ( ( ~ ~ ~ SV2 )
= $true )
| ( SV2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ( ~ ~ ~ $true )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ( ~ ~ ~ $false )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: nat,SV4: nat,SV3: nat] :
( ( ~ ( ( SV3 != SV4 ) )
| ( ( pl @ SV1 @ SV3 )
!= ( pl @ SV1 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $o] :
( ( ( ~ ~ SV2 )
= $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ~ ~ $true )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ( ~ ~ $false )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: nat,SV4: nat,SV3: nat] :
( ( ( ~ ( ( SV3 != SV4 ) ) )
= $true )
| ( ( ( pl @ SV1 @ SV3 )
!= ( pl @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $true )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: nat,SV4: nat,SV3: nat] :
( ( ( SV3 != SV4 )
= $false )
| ( ( ( pl @ SV1 @ SV3 )
!= ( pl @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV1: nat,SV4: nat,SV3: nat] :
( ( ( SV3 = SV4 )
= $true )
| ( ( ( pl @ SV1 @ SV3 )
!= ( pl @ SV1 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV4: nat,SV3: nat,SV1: nat] :
( ( ( ( pl @ SV1 @ SV3 )
= ( pl @ SV1 @ SV4 ) )
= $false )
| ( ( SV3 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,39,37,36,35,17]) ).
thf(41,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM647^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 13:30:00 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.19
% 0.10/0.19 No.of.Axioms: 3
% 0.10/0.19
% 0.10/0.19 Length.of.Defs: 0
% 0.10/0.19
% 0.10/0.19 Contains.Choice.Funs: false
% 0.10/0.19
% 0.10/0.19 ********************************
% 0.10/0.19 * All subproblems solved! *
% 0.10/0.19 ********************************
% 0.10/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.19
% 0.10/0.19 %**** Beginning of derivation protocol ****
% 0.10/0.19 % SZS output start CNFRefutation
% See solution above
% 0.10/0.19
% 0.10/0.19 %**** End of derivation protocol ****
% 0.10/0.19 %**** no. of clauses in derivation: 41 ****
% 0.10/0.19 %**** clause counter: 40 ****
% 0.10/0.19
% 0.10/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:40,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------