TSTP Solution File: SEU305+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : 300s
% DateTime : Thu Aug 31 17:05:39 EDT 2023
% Result : Theorem 2.87s 1.15s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 25 unt; 0 def)
% Number of atoms : 263 ( 61 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 317 ( 118 ~; 115 |; 65 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn; 45 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> join_commut(X0,X1,X2) = join_commut(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(f6,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> join_commut(X0,X1,X2) = join(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(f35,conjecture,
! [X0] :
( ( join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f50,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f54]) ).
fof(f71,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f71]) ).
fof(f74,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f74]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below(X0,X1,X2)
| join(X0,X1,X2) != X2 )
& ( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f101,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( X1 != X2
& below(sK7,X2,X1)
& below(sK7,X1,X2)
& element(X2,the_carrier(sK7)) )
& element(X1,the_carrier(sK7)) )
& join_semilatt_str(sK7)
& join_commutative(sK7)
& ~ empty_carrier(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(sK7,X2,X1)
& below(sK7,X1,X2)
& element(X2,the_carrier(sK7)) )
& element(X1,the_carrier(sK7)) )
=> ( ? [X2] :
( sK8 != X2
& below(sK7,X2,sK8)
& below(sK7,sK8,X2)
& element(X2,the_carrier(sK7)) )
& element(sK8,the_carrier(sK7)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X2] :
( sK8 != X2
& below(sK7,X2,sK8)
& below(sK7,sK8,X2)
& element(X2,the_carrier(sK7)) )
=> ( sK8 != sK9
& below(sK7,sK9,sK8)
& below(sK7,sK8,sK9)
& element(sK9,the_carrier(sK7)) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( sK8 != sK9
& below(sK7,sK9,sK8)
& below(sK7,sK8,sK9)
& element(sK9,the_carrier(sK7))
& element(sK8,the_carrier(sK7))
& join_semilatt_str(sK7)
& join_commutative(sK7)
& ~ empty_carrier(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f75,f103,f102,f101]) ).
fof(f109,plain,
! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f111,plain,
! [X2,X0,X1] :
( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f141,plain,
~ empty_carrier(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f142,plain,
join_commutative(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f143,plain,
join_semilatt_str(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f144,plain,
element(sK8,the_carrier(sK7)),
inference(cnf_transformation,[],[f104]) ).
fof(f145,plain,
element(sK9,the_carrier(sK7)),
inference(cnf_transformation,[],[f104]) ).
fof(f146,plain,
below(sK7,sK8,sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f147,plain,
below(sK7,sK9,sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f148,plain,
sK8 != sK9,
inference(cnf_transformation,[],[f104]) ).
cnf(c_53,plain,
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| join_commut(X1,X0,X2) = join_commut(X1,X2,X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_56,plain,
( ~ below(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| join(X0,X1,X2) = X2
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_80,plain,
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| join_commut(X1,X0,X2) = join(X1,X0,X2)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_85,negated_conjecture,
sK8 != sK9,
inference(cnf_transformation,[],[f148]) ).
cnf(c_86,negated_conjecture,
below(sK7,sK9,sK8),
inference(cnf_transformation,[],[f147]) ).
cnf(c_87,negated_conjecture,
below(sK7,sK8,sK9),
inference(cnf_transformation,[],[f146]) ).
cnf(c_88,negated_conjecture,
element(sK9,the_carrier(sK7)),
inference(cnf_transformation,[],[f145]) ).
cnf(c_89,negated_conjecture,
element(sK8,the_carrier(sK7)),
inference(cnf_transformation,[],[f144]) ).
cnf(c_90,negated_conjecture,
join_semilatt_str(sK7),
inference(cnf_transformation,[],[f143]) ).
cnf(c_91,negated_conjecture,
join_commutative(sK7),
inference(cnf_transformation,[],[f142]) ).
cnf(c_92,negated_conjecture,
~ empty_carrier(sK7),
inference(cnf_transformation,[],[f141]) ).
cnf(c_818,plain,
( X0 != sK7
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| join_commut(X0,X1,X2) = join(X0,X1,X2)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_80,c_91]) ).
cnf(c_819,plain,
( ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7))
| ~ join_semilatt_str(sK7)
| join_commut(sK7,X0,X1) = join(sK7,X0,X1)
| empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_818]) ).
cnf(c_821,plain,
( join_commut(sK7,X0,X1) = join(sK7,X0,X1)
| ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7)) ),
inference(global_subsumption_just,[status(thm)],[c_819,c_90,c_92,c_819]) ).
cnf(c_822,plain,
( ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7))
| join_commut(sK7,X0,X1) = join(sK7,X0,X1) ),
inference(renaming,[status(thm)],[c_821]) ).
cnf(c_848,plain,
( X0 != sK7
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_53,c_91]) ).
cnf(c_849,plain,
( ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7))
| ~ join_semilatt_str(sK7)
| join_commut(sK7,X0,X1) = join_commut(sK7,X1,X0)
| empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_848]) ).
cnf(c_851,plain,
( join_commut(sK7,X0,X1) = join_commut(sK7,X1,X0)
| ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7)) ),
inference(global_subsumption_just,[status(thm)],[c_849,c_90,c_92,c_849]) ).
cnf(c_852,plain,
( ~ element(X0,the_carrier(sK7))
| ~ element(X1,the_carrier(sK7))
| join_commut(sK7,X0,X1) = join_commut(sK7,X1,X0) ),
inference(renaming,[status(thm)],[c_851]) ).
cnf(c_950,plain,
( X0 != sK7
| X1 != sK9
| X2 != sK8
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| join(X0,X1,X2) = X2
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_56,c_86]) ).
cnf(c_951,plain,
( ~ element(sK8,the_carrier(sK7))
| ~ element(sK9,the_carrier(sK7))
| ~ join_semilatt_str(sK7)
| join(sK7,sK9,sK8) = sK8
| empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_950]) ).
cnf(c_952,plain,
join(sK7,sK9,sK8) = sK8,
inference(global_subsumption_just,[status(thm)],[c_951,c_90,c_92,c_89,c_88,c_951]) ).
cnf(c_957,plain,
( X0 != sK7
| X1 != sK8
| X2 != sK9
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| join(X0,X1,X2) = X2
| empty_carrier(X0) ),
inference(resolution_lifted,[status(thm)],[c_56,c_87]) ).
cnf(c_958,plain,
( ~ element(sK8,the_carrier(sK7))
| ~ element(sK9,the_carrier(sK7))
| ~ join_semilatt_str(sK7)
| join(sK7,sK8,sK9) = sK9
| empty_carrier(sK7) ),
inference(unflattening,[status(thm)],[c_957]) ).
cnf(c_959,plain,
join(sK7,sK8,sK9) = sK9,
inference(global_subsumption_just,[status(thm)],[c_958,c_90,c_92,c_89,c_88,c_958]) ).
cnf(c_3628,plain,
( ~ element(X0,the_carrier(sK7))
| join_commut(sK7,X0,sK9) = join(sK7,X0,sK9) ),
inference(superposition,[status(thm)],[c_88,c_822]) ).
cnf(c_3629,plain,
( ~ element(X0,the_carrier(sK7))
| join_commut(sK7,X0,sK8) = join(sK7,X0,sK8) ),
inference(superposition,[status(thm)],[c_89,c_822]) ).
cnf(c_3717,plain,
join_commut(sK7,sK8,sK9) = join(sK7,sK8,sK9),
inference(superposition,[status(thm)],[c_89,c_3628]) ).
cnf(c_3720,plain,
join_commut(sK7,sK8,sK9) = sK9,
inference(light_normalisation,[status(thm)],[c_3717,c_959]) ).
cnf(c_3743,plain,
join_commut(sK7,sK9,sK8) = join(sK7,sK9,sK8),
inference(superposition,[status(thm)],[c_88,c_3629]) ).
cnf(c_3748,plain,
join_commut(sK7,sK9,sK8) = sK8,
inference(light_normalisation,[status(thm)],[c_3743,c_952]) ).
cnf(c_3774,plain,
( ~ element(X0,the_carrier(sK7))
| join_commut(sK7,X0,sK9) = join_commut(sK7,sK9,X0) ),
inference(superposition,[status(thm)],[c_88,c_852]) ).
cnf(c_3811,plain,
join_commut(sK7,sK8,sK9) = join_commut(sK7,sK9,sK8),
inference(superposition,[status(thm)],[c_89,c_3774]) ).
cnf(c_3816,plain,
sK8 = sK9,
inference(light_normalisation,[status(thm)],[c_3811,c_3720,c_3748]) ).
cnf(c_3817,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3816,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 12:31:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.87/1.15 % SZS status Started for theBenchmark.p
% 2.87/1.15 % SZS status Theorem for theBenchmark.p
% 2.87/1.15
% 2.87/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.87/1.15
% 2.87/1.15 ------ iProver source info
% 2.87/1.15
% 2.87/1.15 git: date: 2023-05-31 18:12:56 +0000
% 2.87/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.87/1.15 git: non_committed_changes: false
% 2.87/1.15 git: last_make_outside_of_git: false
% 2.87/1.15
% 2.87/1.15 ------ Parsing...
% 2.87/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.87/1.15
% 2.87/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e
% 2.87/1.15
% 2.87/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.87/1.15
% 2.87/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.87/1.15 ------ Proving...
% 2.87/1.15 ------ Problem Properties
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15 clauses 49
% 2.87/1.15 conjectures 3
% 2.87/1.15 EPR 7
% 2.87/1.15 Horn 44
% 2.87/1.15 unary 21
% 2.87/1.15 binary 11
% 2.87/1.15 lits 114
% 2.87/1.15 lits eq 26
% 2.87/1.15 fd_pure 0
% 2.87/1.15 fd_pseudo 0
% 2.87/1.15 fd_cond 1
% 2.87/1.15 fd_pseudo_cond 1
% 2.87/1.15 AC symbols 0
% 2.87/1.15
% 2.87/1.15 ------ Schedule dynamic 5 is on
% 2.87/1.15
% 2.87/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15 ------
% 2.87/1.15 Current options:
% 2.87/1.15 ------
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15 ------ Proving...
% 2.87/1.15
% 2.87/1.15
% 2.87/1.15 % SZS status Theorem for theBenchmark.p
% 2.87/1.15
% 2.87/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/1.15
% 2.87/1.15
%------------------------------------------------------------------------------