TSTP Solution File: NUM338+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM338+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 : Fri May 3 02:48:42 EDT 2024
% Result : Theorem 129.54s 18.21s
% Output : CNFRefutation 129.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 22 unt; 0 def)
% Number of atoms : 147 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 68 ~; 61 |; 15 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 128 ( 0 sgn 86 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn5) ).
fof(f287,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_pos(X11))
& rdn_add_with_carry(rdnn(n0),X9,X10,X11)
& rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).
fof(f295,axiom,
! [X0,X18,X19,X2] :
( ( sum(X0,X19,X2)
& sum(X0,X18,X2) )
=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_RHS) ).
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus_entry_point) ).
fof(f297,axiom,
! [X20,X21,X22,X23,X24] :
( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f334,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n3_n2_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
! [X0] :
( difference(n5,n3,X0)
=> n2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_n5_n3_only_n2) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( difference(n5,n3,X0)
=> n2 = X0 ),
inference(negated_conjecture,[],[f402]) ).
fof(f411,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X1,rdn_pos(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f287]) ).
fof(f419,plain,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X0,X1,X3) )
=> X1 = X2 ),
inference(rectify,[],[f295]) ).
fof(f420,plain,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
& rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(rectify,[],[f297]) ).
fof(f444,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f411]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(flattening,[],[f444]) ).
fof(f460,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3) ),
inference(ennf_transformation,[],[f419]) ).
fof(f461,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3) ),
inference(flattening,[],[f460]) ).
fof(f462,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(ennf_transformation,[],[f420]) ).
fof(f463,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(flattening,[],[f462]) ).
fof(f471,plain,
? [X0] :
( n2 != X0
& difference(n5,n3,X0) ),
inference(ennf_transformation,[],[f403]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) )
& ( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f475,plain,
( ? [X0] :
( n2 != X0
& difference(n5,n3,X0) )
=> ( n2 != sK0
& difference(n5,n3,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f476,plain,
( n2 != sK0
& difference(n5,n3,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f471,f475]) ).
fof(f479,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f480,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f482,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f765,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f445]) ).
fof(f773,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3) ),
inference(cnf_transformation,[],[f461]) ).
fof(f775,plain,
! [X2,X0,X1] :
( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f474]) ).
fof(f776,plain,
! [X2,X3,X0,X1,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(cnf_transformation,[],[f463]) ).
fof(f813,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f334]) ).
fof(f831,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f881,plain,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f476]) ).
fof(f882,plain,
n2 != sK0,
inference(cnf_transformation,[],[f476]) ).
cnf(c_51,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f479]) ).
cnf(c_52,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f480]) ).
cnf(c_54,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f482]) ).
cnf(c_337,plain,
( ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_translate(X4,rdn_pos(X2))
| ~ rdn_translate(X5,rdn_pos(X1))
| sum(X3,X5,X4) ),
inference(cnf_transformation,[],[f765]) ).
cnf(c_345,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X2)
| X1 = X3 ),
inference(cnf_transformation,[],[f773]) ).
cnf(c_346,plain,
( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f775]) ).
cnf(c_348,plain,
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)) ),
inference(cnf_transformation,[],[f776]) ).
cnf(c_385,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f813]) ).
cnf(c_403,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f831]) ).
cnf(c_453,negated_conjecture,
n2 != sK0,
inference(cnf_transformation,[],[f882]) ).
cnf(c_454,negated_conjecture,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f881]) ).
cnf(c_491,plain,
( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ),
inference(prop_impl_just,[status(thm)],[c_346]) ).
cnf(c_1484,plain,
( X0 != n5
| X1 != n3
| X2 != sK0
| sum(X1,X2,X0) ),
inference(resolution_lifted,[status(thm)],[c_491,c_454]) ).
cnf(c_1485,plain,
sum(n3,sK0,n5),
inference(unflattening,[status(thm)],[c_1484]) ).
cnf(c_4850,plain,
( ~ sum(n3,X0,n5)
| ~ sum(n3,sK0,n5)
| X0 = sK0 ),
inference(instantiation,[status(thm)],[c_345]) ).
cnf(c_12427,plain,
( ~ sum(n3,n2,n5)
| ~ sum(n3,sK0,n5)
| n2 = sK0 ),
inference(instantiation,[status(thm)],[c_4850]) ).
cnf(c_49634,plain,
( ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(n3),rdnn(n2),rdnn(X1)) ),
inference(superposition,[status(thm)],[c_385,c_348]) ).
cnf(c_77542,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
inference(superposition,[status(thm)],[c_403,c_49634]) ).
cnf(c_215679,plain,
( ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_translate(X4,rdn_pos(X2))
| ~ rdn_translate(n2,rdn_pos(X1))
| sum(X3,n2,X4) ),
inference(instantiation,[status(thm)],[c_337]) ).
cnf(c_220765,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(X0,n2,X1) ),
inference(instantiation,[status(thm)],[c_215679]) ).
cnf(c_223434,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| sum(X0,n2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_220765,c_51,c_77542,c_220765]) ).
cnf(c_223435,plain,
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| sum(X0,n2,X1) ),
inference(renaming,[status(thm)],[c_223434]) ).
cnf(c_223437,plain,
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(X0,n2,n5) ),
inference(instantiation,[status(thm)],[c_223435]) ).
cnf(c_228394,plain,
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| sum(X0,n2,n5) ),
inference(global_subsumption_just,[status(thm)],[c_223437,c_54,c_223437]) ).
cnf(c_228397,plain,
( ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(n3,n2,n5) ),
inference(instantiation,[status(thm)],[c_228394]) ).
cnf(c_228398,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_228397,c_12427,c_1485,c_52,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM338+1 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 19:47:27 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 129.54/18.21 % SZS status Started for theBenchmark.p
% 129.54/18.21 % SZS status Theorem for theBenchmark.p
% 129.54/18.21
% 129.54/18.21 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 129.54/18.21
% 129.54/18.21 ------ iProver source info
% 129.54/18.21
% 129.54/18.21 git: date: 2024-05-02 19:28:25 +0000
% 129.54/18.21 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 129.54/18.21 git: non_committed_changes: false
% 129.54/18.21
% 129.54/18.21 ------ Parsing...
% 129.54/18.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 129.54/18.21
% 129.54/18.21 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 129.54/18.21
% 129.54/18.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 129.54/18.21
% 129.54/18.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 129.54/18.21 ------ Proving...
% 129.54/18.21 ------ Problem Properties
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21 clauses 403
% 129.54/18.21 conjectures 1
% 129.54/18.21 EPR 9
% 129.54/18.21 Horn 401
% 129.54/18.21 unary 377
% 129.54/18.21 binary 6
% 129.54/18.21 lits 473
% 129.54/18.21 lits eq 6
% 129.54/18.21 fd_pure 0
% 129.54/18.21 fd_pseudo 0
% 129.54/18.21 fd_cond 0
% 129.54/18.21 fd_pseudo_cond 5
% 129.54/18.21 AC symbols 0
% 129.54/18.21
% 129.54/18.21 ------ Input Options Time Limit: Unbounded
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21 ------
% 129.54/18.21 Current options:
% 129.54/18.21 ------
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21 ------ Proving...
% 129.54/18.21
% 129.54/18.21
% 129.54/18.21 % SZS status Theorem for theBenchmark.p
% 129.54/18.21
% 129.54/18.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 129.54/18.22
% 129.54/18.22
%------------------------------------------------------------------------------