%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM662^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 10:34:50 AM UTC 2026
% Result : Theorem 0.00s 0.12s
% Output : CNFRefutation 0.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 59 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 123 ( 30 ~; 11 |; 0 &; 80 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_sK1_Xx,type,
sK1_Xx: nat ).
thf(tp_sK2_Xx_0,type,
sK2_Xx_0: 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] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz5) ).
thf(2,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).
thf(3,axiom,
~ ! [Xx: nat] :
( z
!= ( pl @ y @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(4,axiom,
~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(5,conjecture,
~ ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(6,negated_conjecture,
( ( ~ ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ~ ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
( ( ~ ! [Xx: nat] :
( z
!= ( pl @ y @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(14,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(15,plain,
( ( z
= ( pl @ y @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,plain,
( ( y
= ( pl @ x @ sK2_Xx_0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(17,plain,
( ( y
= ( pl @ x @ sK2_Xx_0 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(18,plain,
( ( z
= ( pl @ y @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
= ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [Xx_0: nat] :
( z
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
! [SV1: $o] :
( ( ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV2: nat] :
( ( ! [SY7: nat,SY8: nat] :
( ( pl @ ( pl @ SV2 @ SY7 ) @ SY8 )
= ( pl @ SV2 @ ( pl @ SY7 @ SY8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV3: nat] :
( ( z
!= ( pl @ x @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(28,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: nat,SV2: nat] :
( ( ! [SY9: nat] :
( ( pl @ ( pl @ SV2 @ SV4 ) @ SY9 )
= ( pl @ SV2 @ ( pl @ SV4 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV3: nat] :
( ( z
= ( pl @ x @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV5: nat,SV4: nat,SV2: nat] :
( ( ( pl @ ( pl @ SV2 @ SV4 ) @ SV5 )
= ( pl @ SV2 @ ( pl @ SV4 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(36,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,35,34,33,32,31,18]) ).
thf(37,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM662^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % 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 13:32:37 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.12
% 0.00/0.12 No.of.Axioms: 4
% 0.00/0.12
% 0.00/0.12 Length.of.Defs: 0
% 0.00/0.12
% 0.00/0.12 Contains.Choice.Funs: false
% 0.00/0.12
% 0.00/0.12 ********************************
% 0.00/0.12 * All subproblems solved! *
% 0.00/0.12 ********************************
% 0.00/0.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.00/0.12
% 0.00/0.12 %**** Beginning of derivation protocol ****
% 0.00/0.12 % SZS output start CNFRefutation
% See solution above
% 0.00/0.12
% 0.00/0.12 %**** End of derivation protocol ****
% 0.00/0.12 %**** no. of clauses in derivation: 37 ****
% 0.00/0.12 %**** clause counter: 36 ****
% 0.00/0.12
% 0.00/0.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------