%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n015.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 10:44:31 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 50 unt; 0 typ; 29 def)
% Number of atoms : 166 ( 53 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 258 ( 24 ~; 12 |; 14 &; 188 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 4 con; 0-3 aty)
% Number of variables : 92 ( 43 ^; 44 !; 5 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymm,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(tp_asymm,type,
asymm: ( $i > $i > $o ) > $o ).
thf(tp_confl,type,
confl: ( $i > $i > $o ) > $o ).
thf(tp_cr,type,
cr: ( $i > $i > $o ) > $o ).
thf(tp_idem,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_ind,type,
ind: ( $i > $i > $o ) > $o ).
thf(tp_infl,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_innf,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(tp_inv,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_irrefl,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(tp_join,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_lconfl,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(tp_mono,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_nfof,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_norm,type,
norm: ( $i > $i > $o ) > $o ).
thf(tp_po,type,
po: ( $i > $i > $o ) > $o ).
thf(tp_rc,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_refl,type,
refl: ( $i > $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_sc,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_sconfl,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(tp_so,type,
so: ( $i > $i > $o ) > $o ).
thf(tp_subrel,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_symm,type,
symm: ( $i > $i > $o ) > $o ).
thf(tp_tc,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_term,type,
term: ( $i > $i > $o ) > $o ).
thf(tp_total,type,
total: ( $i > $i > $o ) > $o ).
thf(tp_trans,type,
trans: ( $i > $i > $o ) > $o ).
thf(tp_trc,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_trsc,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(antisymm,definition,
( antisymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetric) ).
thf(asymm,definition,
( asymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ~ ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric) ).
thf(confl,definition,
( confl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( trc @ R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',confluent) ).
thf(cr,definition,
( cr
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( trsc @ R @ X @ Y )
=> ( join @ R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_rosser) ).
thf(idem,definition,
( idem
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] :
( ( F @ ( F @ R ) )
= ( F @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotent) ).
thf(ind,definition,
( ind
= ( ^ [R: $i > $i > $o] :
! [P: $i > $o] :
( ! [X: $i] :
( ! [Y: $i] :
( ( tc @ R @ X @ Y )
=> ( P @ Y ) )
=> ( P @ X ) )
=> ! [X: $i] : ( P @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfying_the_induction_principle) ).
thf(infl,definition,
( infl
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] : ( subrel @ R @ ( F @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inflationary) ).
thf(innf,definition,
( innf
= ( ^ [R: $i > $i > $o,X: $i] :
~ ? [Y: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_normal_form) ).
thf(inv,definition,
( inv
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(irrefl,definition,
( irrefl
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive) ).
thf(join,definition,
( join
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
? [Z: $i] :
( ( trc @ R @ X @ Z )
& ( trc @ R @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',joinable) ).
thf(lconfl,definition,
( lconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',locally_confluent) ).
thf(mono,definition,
( mono
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o,S: $i > $i > $o] :
( ( subrel @ R @ S )
=> ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotonic) ).
thf(nfof,definition,
( nfof
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( trc @ R @ Y @ X )
& ( innf @ R @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normal_form_of) ).
thf(norm,definition,
( norm
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
? [Y: $i] : ( nfof @ R @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalizing) ).
thf(po,definition,
( po
= ( ^ [R: $i > $i > $o] :
( ( refl @ R )
& ( antisymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order) ).
thf(rc,definition,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexive_closure) ).
thf(refl,definition,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexive) ).
thf(sc,definition,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure) ).
thf(sconfl,definition,
( sconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',semi_confluent) ).
thf(so,definition,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).
thf(subrel,definition,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subrel) ).
thf(symm,definition,
( symm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric) ).
thf(tc,definition,
( tc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
! [S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S ) )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure) ).
thf(term,definition,
( term
= ( ^ [R: $i > $i > $o] :
! [A: $i > $o] :
( ? [X: $i] : ( A @ X )
=> ? [X: $i] :
( ( A @ X )
& ! [Y: $i] :
( ( A @ Y )
=> ~ ( R @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',terminating) ).
thf(total,definition,
( total
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y )
| ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total) ).
thf(trans,definition,
( trans
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive) ).
thf(trc,definition,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_closure) ).
thf(trsc,definition,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure) ).
thf(1,conjecture,
infl @ sc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_inflationary) ).
thf(2,negated_conjecture,
( ( infl @ sc )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o,SY6: $i,SY7: $i] :
( ( SY0 @ SY6 @ SY7 )
=> ( ( SY0 @ SY7 @ SY6 )
| ( SY0 @ SY6 @ SY7 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,antisymm,asymm,confl,cr,idem,ind,infl,innf,inv,irrefl,join,lconfl,mono,nfof,norm,po,rc,refl,sc,sconfl,so,subrel,symm,tc,term,total,trans,trc,trsc]) ).
thf(4,plain,
( ( ! [SY12: $i,SY13: $i] :
( ( sK1_SY0 @ SY12 @ SY13 )
=> ( ( sK1_SY0 @ SY13 @ SY12 )
| ( sK1_SY0 @ SY12 @ SY13 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY14: $i] :
( ( sK1_SY0 @ sK2_SY12 @ SY14 )
=> ( ( sK1_SY0 @ SY14 @ sK2_SY12 )
| ( sK1_SY0 @ sK2_SY12 @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 )
=> ( ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
| ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
| ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
| ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
& ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(12,plain,
( ( ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
& ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ~ ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,antisymm,asymm,confl,cr,idem,ind,infl,innf,inv,irrefl,join,lconfl,mono,nfof,norm,po,rc,refl,sc,sconfl,so,subrel,symm,tc,term,total,trans,trc,trsc]) ).
thf(14,plain,
( ( ~ ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
( ( ~ ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( sK1_SY0 @ sK3_SY14 @ sK2_SY12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( sK1_SY0 @ sK2_SY12 @ sK3_SY14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,20,19]) ).
thf(22,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 15:28:43 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 0
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 5096
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 22 ****
% 0.07/0.24 %**** clause counter: 21 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------