%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM696^1 : 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 : 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 10:34:58 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 112 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 279 ( 53 ~; 23 |; 0 &; 194 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_n_1,type,
n_1: nat ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_sK1_Xx_0,type,
sK1_Xx_0: nat > nat > nat > nat ).
thf(tp_sK2_Xx_0,type,
sK2_Xx_0: nat > nat ).
thf(tp_sK3_Xx_0,type,
sK3_Xx_0: nat ).
thf(tp_x,type,
x: nat ).
thf(tp_y,type,
y: nat ).
thf(1,axiom,
! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(2,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ Xy @ Xx_0 ) )
=> ~ ! [Xx_0: nat] :
( ( pl @ Xx @ Xz )
!= ( pl @ ( pl @ Xy @ Xz ) @ Xx_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(3,axiom,
! [Xx: nat] :
( ~ ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ n_1 @ Xx_0 ) )
=> ( Xx = n_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).
thf(4,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',et) ).
thf(5,axiom,
~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(6,conjecture,
( ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25) ).
thf(7,negated_conjecture,
( ( ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) )
=> ( y
= ( pl @ x @ n_1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ Xy @ Xx_0 ) )
=> ~ ! [Xx_0: nat] :
( ( pl @ Xx @ Xz )
!= ( pl @ ( pl @ Xy @ Xz ) @ Xx_0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [Xx: nat] :
( ~ ~ ! [Xx_0: nat] :
( Xx
!= ( pl @ n_1 @ Xx_0 ) )
=> ( Xx = n_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ! [Xx_0: nat] :
( y
!= ( pl @ x @ Xx_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ~ ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(15,plain,
( ( y
= ( pl @ x @ n_1 ) )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(16,plain,
( ( y
!= ( pl @ x @ n_1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xx_0: nat] :
( Xx
!= ( pl @ Xy @ Xx_0 ) )
| ! [Xz: nat] :
( ( pl @ Xx @ Xz )
= ( pl @ ( pl @ Xy @ Xz ) @ ( sK1_Xx_0 @ Xz @ Xy @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(19,plain,
( ( ! [Xx: nat] :
( ( Xx
= ( pl @ n_1 @ ( sK2_Xx_0 @ Xx ) ) )
| ( Xx = n_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(20,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(21,plain,
( ( y
= ( pl @ x @ sK3_Xx_0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(22,plain,
( ( y
= ( pl @ x @ sK3_Xx_0 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [Xa: $o] :
( ~ Xa
| Xa ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [Xx: nat] :
( ( Xx
= ( pl @ n_1 @ ( sK2_Xx_0 @ Xx ) ) )
| ( Xx = n_1 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(25,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xx_0: nat] :
( Xx
!= ( pl @ Xy @ Xx_0 ) )
| ! [Xz: nat] :
( ( pl @ Xx @ Xz )
= ( pl @ ( pl @ Xy @ Xz ) @ ( sK1_Xx_0 @ Xz @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [Xx_0: nat] :
( y
!= ( pl @ ( pl @ x @ n_1 ) @ Xx_0 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(28,plain,
( ( y
!= ( pl @ x @ n_1 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
! [SV1: $o] :
( ( ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(31,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[23]) ).
thf(32,plain,
! [SV2: nat] :
( ( ( SV2
= ( pl @ n_1 @ ( sK2_Xx_0 @ SV2 ) ) )
| ( SV2 = n_1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(33,plain,
! [SV3: nat] :
( ( ! [SY12: nat] :
( ! [SY13: nat] :
( SV3
!= ( pl @ SY12 @ SY13 ) )
| ! [SY14: nat] :
( ( pl @ SV3 @ SY14 )
= ( pl @ ( pl @ SY12 @ SY14 ) @ ( sK1_Xx_0 @ SY14 @ SY12 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
! [SV4: nat] :
( ( ! [SY15: nat] :
( ( pl @ SV4 @ SY15 )
= ( pl @ SY15 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV5: nat] :
( ( y
!= ( pl @ ( pl @ x @ n_1 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
( ( y
= ( pl @ x @ n_1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(38,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(39,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV2: nat] :
( ( ( SV2
= ( pl @ n_1 @ ( sK2_Xx_0 @ SV2 ) ) )
= $true )
| ( ( SV2 = n_1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV6: nat,SV3: nat] :
( ( ! [SY16: nat] :
( SV3
!= ( pl @ SV6 @ SY16 ) )
| ! [SY17: nat] :
( ( pl @ SV3 @ SY17 )
= ( pl @ ( pl @ SV6 @ SY17 ) @ ( sK1_Xx_0 @ SY17 @ SV6 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV7: nat,SV4: nat] :
( ( ( pl @ SV4 @ SV7 )
= ( pl @ SV7 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV5: nat] :
( ( y
= ( pl @ ( pl @ x @ n_1 ) @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(45,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(46,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV6: nat,SV3: nat] :
( ( ( ! [SY16: nat] :
( SV3
!= ( pl @ SV6 @ SY16 ) ) )
= $true )
| ( ( ! [SY17: nat] :
( ( pl @ SV3 @ SY17 )
= ( pl @ ( pl @ SV6 @ SY17 ) @ ( sK1_Xx_0 @ SY17 @ SV6 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV8: nat,SV6: nat,SV3: nat] :
( ( ( SV3
!= ( pl @ SV6 @ SV8 ) )
= $true )
| ( ( ! [SY17: nat] :
( ( pl @ SV3 @ SY17 )
= ( pl @ ( pl @ SV6 @ SY17 ) @ ( sK1_Xx_0 @ SY17 @ SV6 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV8: nat,SV6: nat,SV3: nat] :
( ( ( SV3
= ( pl @ SV6 @ SV8 ) )
= $false )
| ( ( ! [SY17: nat] :
( ( pl @ SV3 @ SY17 )
= ( pl @ ( pl @ SV6 @ SY17 ) @ ( sK1_Xx_0 @ SY17 @ SV6 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV8: nat,SV6: nat,SV9: nat,SV3: nat] :
( ( ( ( pl @ SV3 @ SV9 )
= ( pl @ ( pl @ SV6 @ SV9 ) @ ( sK1_Xx_0 @ SV9 @ SV6 @ SV3 ) ) )
= $true )
| ( ( SV3
= ( pl @ SV6 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,50,46,45,44,43,42,40,36]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM696^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 13:35:40 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.24
% 0.10/0.24 No.of.Axioms: 5
% 0.10/0.24
% 0.10/0.24 Length.of.Defs: 0
% 0.10/0.24
% 0.10/0.24 Contains.Choice.Funs: false
% 0.10/0.24 .
% 0.10/0.24
% 0.10/0.24 ********************************
% 0.10/0.24 * All subproblems solved! *
% 0.10/0.24 ********************************
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.24
% 0.10/0.24 %**** Beginning of derivation protocol ****
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24
% 0.10/0.24 %**** End of derivation protocol ****
% 0.10/0.24 %**** no. of clauses in derivation: 52 ****
% 0.10/0.24 %**** clause counter: 51 ****
% 0.10/0.24
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------