%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM687^1 : 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 : n018.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 10:34:55 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 279 ( 100 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 420 ( 74 ~; 56 |; 0 &; 272 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 105 ( 0 ^; 105 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_more,type,
more: nat > nat > $o ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_u,type,
u: 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,Xu: nat] :
( ( more @ Xx @ Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(2,axiom,
! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( Xx = Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19g) ).
thf(3,axiom,
! [Xa: $o] :
( ~ ~ Xa
=> Xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).
thf(4,axiom,
more @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(5,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(6,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).
thf(7,negated_conjecture,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( more @ Xx @ Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( Xx = Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( more @ z @ u )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ( more @ x @ y )
=> ( x = y ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ~ ( more @ x @ y )
=> ( x = y ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( more @ z @ u )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [Xa: $o] :
( ~ ~ Xa
=> Xa ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( Xx = Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( more @ Xx @ Xy )
=> ( ( more @ Xz @ Xu )
=> ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ~ ( more @ x @ y )
| ( x = y ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(22,plain,
( ( ! [SX0: $o] :
( ~ ~ ~ SX0
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( more @ SX0 @ SX1 )
| ~ ( more @ SX2 @ SX3 )
| ( more @ ( pl @ SX0 @ SX2 ) @ ( pl @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( SX0 != SX1 )
| ~ ( more @ SX2 @ SX3 )
| ( more @ ( pl @ SX0 @ SX2 ) @ ( pl @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(25,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ( ~ ~ ( more @ x @ y ) )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV1: $o] :
( ( ~ ~ ~ SV1
| SV1 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[22]) ).
thf(28,plain,
( ( ~ ~ ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ~ ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV2: nat] :
( ( ! [SY9: nat,SY10: nat,SY11: nat] :
( ~ ( more @ SV2 @ SY9 )
| ~ ( more @ SY10 @ SY11 )
| ( more @ ( pl @ SV2 @ SY10 ) @ ( pl @ SY9 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV3: nat] :
( ( ! [SY12: nat,SY13: nat,SY14: nat] :
( ( SV3 != SY12 )
| ~ ( more @ SY13 @ SY14 )
| ( more @ ( pl @ SV3 @ SY13 ) @ ( pl @ SY12 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
( ( ( ~ ( more @ x @ y ) )
= $false )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV1: $o] :
( ( ( ~ ~ ~ SV1 )
= $true )
| ( SV1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( ( ~ ~ ~ $true )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
( ( ( ~ ~ ~ $false )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV4: nat,SV2: nat] :
( ( ! [SY15: nat,SY16: nat] :
( ~ ( more @ SV2 @ SV4 )
| ~ ( more @ SY15 @ SY16 )
| ( more @ ( pl @ SV2 @ SY15 ) @ ( pl @ SV4 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV5: nat,SV3: nat] :
( ( ! [SY17: nat,SY18: nat] :
( ( SV3 != SV5 )
| ~ ( more @ SY17 @ SY18 )
| ( more @ ( pl @ SV3 @ SY17 ) @ ( pl @ SV5 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ( more @ x @ y )
= $true )
| ( ( x = y )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(39,plain,
! [SV1: $o] :
( ( ( ~ ~ SV1 )
= $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ( ~ ~ $true )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( ( ~ ~ $false )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV6: nat,SV4: nat,SV2: nat] :
( ( ! [SY19: nat] :
( ~ ( more @ SV2 @ SV4 )
| ~ ( more @ SV6 @ SY19 )
| ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV7: nat,SV5: nat,SV3: nat] :
( ( ! [SY20: nat] :
( ( SV3 != SV5 )
| ~ ( more @ SV7 @ SY20 )
| ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV1: $o] :
( ( ( ~ SV1 ) = $true )
| ( SV1 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV8: nat,SV6: nat,SV4: nat,SV2: nat] :
( ( ~ ( more @ SV2 @ SV4 )
| ~ ( more @ SV6 @ SV8 )
| ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV9: nat,SV7: nat,SV5: nat,SV3: nat] :
( ( ( SV3 != SV5 )
| ~ ( more @ SV7 @ SV9 )
| ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( SV1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV8: nat,SV6: nat,SV4: nat,SV2: nat] :
( ( ( ~ ( more @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( more @ SV6 @ SV8 )
| ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV9: nat,SV7: nat,SV5: nat,SV3: nat] :
( ( ( SV3 != SV5 )
= $true )
| ( ( ~ ( more @ SV7 @ SV9 )
| ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV8: nat,SV6: nat,SV4: nat,SV2: nat] :
( ( ( more @ SV2 @ SV4 )
= $false )
| ( ( ~ ( more @ SV6 @ SV8 )
| ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV9: nat,SV7: nat,SV5: nat,SV3: nat] :
( ( ( SV3 = SV5 )
= $false )
| ( ( ~ ( more @ SV7 @ SV9 )
| ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV4: nat,SV2: nat,SV8: nat,SV6: nat] :
( ( ( ~ ( more @ SV6 @ SV8 ) )
= $true )
| ( ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SV8 ) )
= $true )
| ( ( more @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV5: nat,SV3: nat,SV9: nat,SV7: nat] :
( ( ( ~ ( more @ SV7 @ SV9 ) )
= $true )
| ( ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SV9 ) )
= $true )
| ( ( SV3 = SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV4: nat,SV2: nat,SV8: nat,SV6: nat] :
( ( ( more @ SV6 @ SV8 )
= $false )
| ( ( more @ ( pl @ SV2 @ SV6 ) @ ( pl @ SV4 @ SV8 ) )
= $true )
| ( ( more @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV5: nat,SV3: nat,SV9: nat,SV7: nat] :
( ( ( more @ SV7 @ SV9 )
= $false )
| ( ( more @ ( pl @ SV3 @ SV7 ) @ ( pl @ SV5 @ SV9 ) )
= $true )
| ( ( SV3 = SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,59,58,51,50,49,38,25]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM687^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 13:36:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 5
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 .
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 61 ****
% 0.09/0.23 %**** clause counter: 60 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------