TSTP Solution File: NUM754^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM754^1 : 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 11:55:04 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 29 unt; 8 typ; 0 def)
% Number of atoms : 233 ( 61 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 416 ( 40 ~; 56 |; 0 &; 310 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 114 ( 0 ^ 114 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_moref,type,
moref: frac > frac > $o ).
thf(tp_pf,type,
pf: frac > frac > frac ).
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] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(2,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( moref @ Xz @ Xu )
=> ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62g) ).
thf(3,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( moref @ Xx @ Xy )
=> ( ( eq @ Xx @ Xz )
=> ( ( eq @ Xy @ Xu )
=> ( moref @ Xz @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(4,axiom,
moref @ z @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(5,axiom,
eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(6,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62h) ).
thf(7,negated_conjecture,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( moref @ Xz @ Xu )
=> ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
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)],[3]) ).
thf(12,plain,
( ( moref @ z @ u )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( eq @ x @ y )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac,Xu: frac] :
( ~ ( moref @ Xz @ Xu )
| ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(16,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(17,plain,
( ( eq @ x @ y )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(18,plain,
( ( moref @ z @ u )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,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)],[16]) ).
thf(20,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac,Xu: frac] :
( ~ ( moref @ Xz @ Xu )
| ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(22,plain,
( ( ~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
! [SV1: frac] :
( ( ! [SY10: frac] :
( ~ ( moref @ SV1 @ SY10 )
| ! [SY11: frac] :
( ~ ( eq @ SV1 @ SY11 )
| ! [Xu: frac] :
( ~ ( eq @ SY10 @ Xu )
| ( moref @ SY11 @ Xu ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: frac] :
( ( ! [SY13: frac] :
( ~ ( eq @ SV2 @ SY13 )
| ! [SY14: frac,SY15: frac] :
( ~ ( moref @ SY14 @ SY15 )
| ( moref @ ( pf @ SV2 @ SY14 ) @ ( pf @ SY13 @ SY15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: frac] :
( ( ! [SY16: frac] : ( eq @ ( pf @ SV3 @ SY16 ) @ ( pf @ SY16 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: frac,SV1: frac] :
( ( ~ ( moref @ SV1 @ SV4 )
| ! [SY17: frac] :
( ~ ( eq @ SV1 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV4 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV5: frac,SV2: frac] :
( ( ~ ( eq @ SV2 @ SV5 )
| ! [SY19: frac,SY20: frac] :
( ~ ( moref @ SY19 @ SY20 )
| ( moref @ ( pf @ SV2 @ SY19 ) @ ( pf @ SV5 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV6: frac,SV3: frac] :
( ( eq @ ( pf @ SV3 @ SV6 ) @ ( pf @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: frac,SV1: frac] :
( ( ( ~ ( moref @ SV1 @ SV4 ) )
= $true )
| ( ( ! [SY17: frac] :
( ~ ( eq @ SV1 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV4 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV5: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY19: frac,SY20: frac] :
( ~ ( moref @ SY19 @ SY20 )
| ( moref @ ( pf @ SV2 @ SY19 ) @ ( pf @ SV5 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: frac,SV1: frac] :
( ( ( moref @ SV1 @ SV4 )
= $false )
| ( ( ! [SY17: frac] :
( ~ ( eq @ SV1 @ SY17 )
| ! [SY18: frac] :
( ~ ( eq @ SV4 @ SY18 )
| ( moref @ SY17 @ SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV5: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV5 )
= $false )
| ( ( ! [SY19: frac,SY20: frac] :
( ~ ( moref @ SY19 @ SY20 )
| ( moref @ ( pf @ SV2 @ SY19 ) @ ( pf @ SV5 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: frac,SV7: frac,SV1: frac] :
( ( ( ~ ( eq @ SV1 @ SV7 )
| ! [SY21: frac] :
( ~ ( eq @ SV4 @ SY21 )
| ( moref @ SV7 @ SY21 ) ) )
= $true )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: frac,SV2: frac,SV8: frac] :
( ( ( ! [SY22: frac] :
( ~ ( moref @ SV8 @ SY22 )
| ( moref @ ( pf @ SV2 @ SV8 ) @ ( pf @ SV5 @ SY22 ) ) ) )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: frac,SV7: frac,SV1: frac] :
( ( ( ~ ( eq @ SV1 @ SV7 ) )
= $true )
| ( ( ! [SY21: frac] :
( ~ ( eq @ SV4 @ SY21 )
| ( moref @ SV7 @ SY21 ) ) )
= $true )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: frac,SV2: frac,SV9: frac,SV8: frac] :
( ( ( ~ ( moref @ SV8 @ SV9 )
| ( moref @ ( pf @ SV2 @ SV8 ) @ ( pf @ SV5 @ SV9 ) ) )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: frac,SV7: frac,SV1: frac] :
( ( ( eq @ SV1 @ SV7 )
= $false )
| ( ( ! [SY21: frac] :
( ~ ( eq @ SV4 @ SY21 )
| ( moref @ SV7 @ SY21 ) ) )
= $true )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV5: frac,SV2: frac,SV9: frac,SV8: frac] :
( ( ( ~ ( moref @ SV8 @ SV9 ) )
= $true )
| ( ( moref @ ( pf @ SV2 @ SV8 ) @ ( pf @ SV5 @ SV9 ) )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: frac,SV7: frac,SV10: frac,SV4: frac] :
( ( ( ~ ( eq @ SV4 @ SV10 )
| ( moref @ SV7 @ SV10 ) )
= $true )
| ( ( eq @ SV1 @ SV7 )
= $false )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: frac,SV2: frac,SV9: frac,SV8: frac] :
( ( ( moref @ SV8 @ SV9 )
= $false )
| ( ( moref @ ( pf @ SV2 @ SV8 ) @ ( pf @ SV5 @ SV9 ) )
= $true )
| ( ( eq @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV1: frac,SV7: frac,SV10: frac,SV4: frac] :
( ( ( ~ ( eq @ SV4 @ SV10 ) )
= $true )
| ( ( moref @ SV7 @ SV10 )
= $true )
| ( ( eq @ SV1 @ SV7 )
= $false )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV1: frac,SV7: frac,SV10: frac,SV4: frac] :
( ( ( eq @ SV4 @ SV10 )
= $false )
| ( ( moref @ SV7 @ SV10 )
= $true )
| ( ( eq @ SV1 @ SV7 )
= $false )
| ( ( moref @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,43,41,29,26,18]) ).
thf(45,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM754^1 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jul 6 10:42:33 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 5
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.41
% 0.20/0.41 ********************************
% 0.20/0.41 * All subproblems solved! *
% 0.20/0.41 ********************************
% 0.20/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:44,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.41
% 0.20/0.41 %**** Beginning of derivation protocol ****
% 0.20/0.41 % SZS output start CNFRefutation
% See solution above
% 0.20/0.41
% 0.20/0.41 %**** End of derivation protocol ****
% 0.20/0.41 %**** no. of clauses in derivation: 45 ****
% 0.20/0.41 %**** clause counter: 44 ****
% 0.20/0.41
% 0.20/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------