TSTP Solution File: NUM738^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM738^1 : 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 : n029.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 11:54:50 EDT 2022
% Result : Theorem 0.18s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 32 unt; 8 typ; 0 def)
% Number of atoms : 221 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 300 ( 36 ~; 48 |; 0 &; 206 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 0 ^ 88 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_lessf,type,
lessf: frac > frac > $o ).
thf(tp_moref,type,
moref: frac > frac > $o ).
thf(tp_u,type,
u: frac ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(tp_z,type,
z: frac ).
thf(1,axiom,
! [Xx: frac,Xy: frac] :
( ( lessf @ Xx @ Xy )
=> ( moref @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz43) ).
thf(2,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( moref @ Xx @ Xy )
=> ( ( eq @ Xx @ Xz )
=> ( ( eq @ Xy @ Xu )
=> ( moref @ Xz @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(3,axiom,
! [Xx: frac,Xy: frac] :
( ( moref @ Xx @ Xy )
=> ( lessf @ Xy @ Xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz42) ).
thf(4,axiom,
eq @ y @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(5,axiom,
eq @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(6,axiom,
lessf @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(7,conjecture,
lessf @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45) ).
thf(8,negated_conjecture,
( ( lessf @ z @ u )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( lessf @ z @ u )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [Xx: frac,Xy: frac] :
( ( lessf @ Xx @ Xy )
=> ( moref @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( moref @ Xx @ Xy )
=> ( ( eq @ Xx @ Xz )
=> ( ( eq @ Xy @ Xu )
=> ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [Xx: frac,Xy: frac] :
( ( moref @ Xx @ Xy )
=> ( lessf @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( eq @ y @ u )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( eq @ x @ z )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( lessf @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ~ ( lessf @ z @ u ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( lessf @ Xx @ Xy )
| ( moref @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xx @ Xz )
| ! [Xu: frac] :
( ~ ( eq @ Xy @ Xu )
| ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(19,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ( lessf @ Xy @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(20,plain,
( ( lessf @ x @ y )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( eq @ x @ z )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
( ( eq @ y @ u )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(23,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ( lessf @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( moref @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xx @ Xz )
| ! [Xu: frac] :
( ~ ( eq @ Xy @ Xu )
| ( moref @ Xz @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( lessf @ Xx @ Xy )
| ( moref @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ~ ( lessf @ z @ u ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
! [SV1: frac] :
( ( ! [SY8: frac] :
( ~ ( moref @ SV1 @ SY8 )
| ( lessf @ SY8 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: frac] :
( ( ! [SY9: frac] :
( ~ ( moref @ SV2 @ SY9 )
| ! [SY10: frac] :
( ~ ( eq @ SV2 @ SY10 )
| ! [Xu: frac] :
( ~ ( eq @ SY9 @ Xu )
| ( moref @ SY10 @ Xu ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: frac] :
( ( ! [SY12: frac] :
( ~ ( lessf @ SV3 @ SY12 )
| ( moref @ SY12 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( lessf @ z @ u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: frac,SV1: frac] :
( ( ~ ( moref @ SV1 @ SV4 )
| ( lessf @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: frac,SV2: frac] :
( ( ~ ( moref @ SV2 @ SV5 )
| ! [SY13: frac] :
( ~ ( eq @ SV2 @ SY13 )
| ! [SY14: frac] :
( ~ ( eq @ SV5 @ SY14 )
| ( moref @ SY13 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV6: frac,SV3: frac] :
( ( ~ ( lessf @ SV3 @ SV6 )
| ( moref @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: frac,SV1: frac] :
( ( ( ~ ( moref @ SV1 @ SV4 ) )
= $true )
| ( ( lessf @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV5: frac,SV2: frac] :
( ( ( ~ ( moref @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY13: frac] :
( ~ ( eq @ SV2 @ SY13 )
| ! [SY14: frac] :
( ~ ( eq @ SV5 @ SY14 )
| ( moref @ SY13 @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV6: frac,SV3: frac] :
( ( ( ~ ( lessf @ SV3 @ SV6 ) )
= $true )
| ( ( moref @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: frac,SV1: frac] :
( ( ( moref @ SV1 @ SV4 )
= $false )
| ( ( lessf @ SV4 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV5: frac,SV2: frac] :
( ( ( moref @ SV2 @ SV5 )
= $false )
| ( ( ! [SY13: frac] :
( ~ ( eq @ SV2 @ SY13 )
| ! [SY14: frac] :
( ~ ( eq @ SV5 @ SY14 )
| ( moref @ SY13 @ SY14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV6: frac,SV3: frac] :
( ( ( lessf @ SV3 @ SV6 )
= $false )
| ( ( moref @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: frac,SV7: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV7 )
| ! [SY15: frac] :
( ~ ( eq @ SV5 @ SY15 )
| ( moref @ SV7 @ SY15 ) ) )
= $true )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: frac,SV7: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV7 ) )
= $true )
| ( ( ! [SY15: frac] :
( ~ ( eq @ SV5 @ SY15 )
| ( moref @ SV7 @ SY15 ) ) )
= $true )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV5: frac,SV7: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV7 )
= $false )
| ( ( ! [SY15: frac] :
( ~ ( eq @ SV5 @ SY15 )
| ( moref @ SV7 @ SY15 ) ) )
= $true )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV2: frac,SV7: frac,SV8: frac,SV5: frac] :
( ( ( ~ ( eq @ SV5 @ SV8 )
| ( moref @ SV7 @ SV8 ) )
= $true )
| ( ( eq @ SV2 @ SV7 )
= $false )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV2: frac,SV7: frac,SV8: frac,SV5: frac] :
( ( ( ~ ( eq @ SV5 @ SV8 ) )
= $true )
| ( ( moref @ SV7 @ SV8 )
= $true )
| ( ( eq @ SV2 @ SV7 )
= $false )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(45,plain,
! [SV2: frac,SV7: frac,SV8: frac,SV5: frac] :
( ( ( eq @ SV5 @ SV8 )
= $false )
| ( ( moref @ SV7 @ SV8 )
= $true )
| ( ( eq @ SV2 @ SV7 )
= $false )
| ( ( moref @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,45,39,37,30,22,21]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM738^1 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 01:18:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 6
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.18/0.37
% 0.18/0.37 ********************************
% 0.18/0.37 * All subproblems solved! *
% 0.18/0.37 ********************************
% 0.18/0.37 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.38
% 0.18/0.38 %**** Beginning of derivation protocol ****
% 0.18/0.38 % SZS output start CNFRefutation
% See solution above
% 0.18/0.38
% 0.18/0.38 %**** End of derivation protocol ****
% 0.18/0.38 %**** no. of clauses in derivation: 47 ****
% 0.18/0.38 %**** clause counter: 46 ****
% 0.18/0.38
% 0.18/0.38 % SZS status Theorem for /export/starexec/sandbox2/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------