TSTP Solution File: NUM677^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM677^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:54:06 EDT 2022
% Result : Theorem 0.22s 0.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 24 unt; 7 typ; 0 def)
% Number of atoms : 121 ( 53 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 198 ( 16 ~; 20 |; 0 &; 158 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 0 ^ 58 !; 0 ?; 58 :)
% 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] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
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,
more @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(4,axiom,
x = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).
thf(5,conjecture,
more @ ( pl @ z @ x ) @ ( pl @ u @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19h) ).
thf(6,negated_conjecture,
( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,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(10,plain,
( ( more @ z @ u )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( x = y )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
| ! [Xz: nat,Xu: nat] :
( ~ ( more @ Xz @ Xu )
| ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(14,plain,
( ( x = y )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( more @ z @ u )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( Xx != Xy )
| ! [Xz: nat,Xu: nat] :
( ~ ( more @ Xz @ Xu )
| ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( pl @ Xx @ Xy )
= ( pl @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
! [SV1: nat] :
( ( ! [SY6: nat] :
( ( SV1 != SY6 )
| ! [SY7: nat,SY8: nat] :
( ~ ( more @ SY7 @ SY8 )
| ( more @ ( pl @ SV1 @ SY7 ) @ ( pl @ SY6 @ SY8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: nat] :
( ( ! [SY9: nat] :
( ( pl @ SV2 @ SY9 )
= ( pl @ SY9 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( more @ ( pl @ z @ x ) @ ( pl @ u @ y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: nat,SV1: nat] :
( ( ( SV1 != SV3 )
| ! [SY10: nat,SY11: nat] :
( ~ ( more @ SY10 @ SY11 )
| ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: nat,SV2: nat] :
( ( ( pl @ SV2 @ SV4 )
= ( pl @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: nat,SV1: nat] :
( ( ( ( SV1 != SV3 ) )
= $true )
| ( ( ! [SY10: nat,SY11: nat] :
( ~ ( more @ SY10 @ SY11 )
| ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV3: nat,SV1: nat] :
( ( ( SV1 = SV3 )
= $false )
| ( ( ! [SY10: nat,SY11: nat] :
( ~ ( more @ SY10 @ SY11 )
| ( more @ ( pl @ SV1 @ SY10 ) @ ( pl @ SV3 @ SY11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV3: nat,SV1: nat,SV5: nat] :
( ( ( ! [SY12: nat] :
( ~ ( more @ SV5 @ SY12 )
| ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SY12 ) ) ) )
= $true )
| ( ( SV1 = SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(27,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( ~ ( more @ SV5 @ SV6 )
| ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) ) )
= $true )
| ( ( SV1 = SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( ~ ( more @ SV5 @ SV6 ) )
= $true )
| ( ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) )
= $true )
| ( ( SV1 = SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV3: nat,SV1: nat,SV6: nat,SV5: nat] :
( ( ( more @ SV5 @ SV6 )
= $false )
| ( ( more @ ( pl @ SV1 @ SV5 ) @ ( pl @ SV3 @ SV6 ) )
= $true )
| ( ( SV1 = SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[14,29,23,21,15]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM677^1 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jul 6 05:09:33 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37
% 0.15/0.37 No.of.Axioms: 4
% 0.15/0.37
% 0.15/0.37 Length.of.Defs: 0
% 0.15/0.37
% 0.15/0.37 Contains.Choice.Funs: false
% 0.15/0.37 (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.22/0.40
% 0.22/0.40 ********************************
% 0.22/0.40 * All subproblems solved! *
% 0.22/0.40 ********************************
% 0.22/0.40 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.40
% 0.22/0.40 %**** Beginning of derivation protocol ****
% 0.22/0.40 % SZS output start CNFRefutation
% See solution above
% 0.22/0.40
% 0.22/0.40 %**** End of derivation protocol ****
% 0.22/0.40 %**** no. of clauses in derivation: 31 ****
% 0.22/0.40 %**** clause counter: 30 ****
% 0.22/0.40
% 0.22/0.40 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------