%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM316+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:23:41 PM UTC 2026
% Result : Theorem 12.54s 18.28s
% Output : CNFRefutation 12.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 34 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 56 ~; 52 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn3) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X1),rdnn(X2))
& rdn_positive_less(rdnn(X0),rdnn(X1)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(f289,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_neg(X5))
& rdn_add_with_carry(rdnn(n0),X3,X5,X4)
& rdn_positive_less(X3,X4)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_1) ).
fof(f297,axiom,
! [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)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
sum(n2,nn5,nn3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_nn5_nn3) ).
fof(f403,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(n2,nn5,nn3),
inference(flattening,[],[f403]) ).
fof(f406,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f407,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(flattening,[],[f406]) ).
fof(f428,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(ennf_transformation,[],[f289]) ).
fof(f429,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(flattening,[],[f428]) ).
fof(f442,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(ennf_transformation,[],[f297]) ).
fof(f443,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(flattening,[],[f442]) ).
fof(f456,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f584,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f131]) ).
fof(f586,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f721,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f722,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f723,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f270]) ).
fof(f728,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[],[f407]) ).
fof(f744,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f429]) ).
fof(f753,plain,
! [X2,X3,X0,X1,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(cnf_transformation,[],[f443]) ).
fof(f781,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f808,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f858,plain,
~ sum(n2,nn5,nn3),
inference(cnf_transformation,[],[f404]) ).
tcf(c_51,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f456]) ).
tcf(c_179,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f584]) ).
tcf(c_181,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f586]) ).
tcf(c_316,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f721]) ).
tcf(c_317,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f722]) ).
tcf(c_318,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f723]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[],[f728]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,X5,X4)
| ~ rdn_positive_less(X0,X2)
| ~ rdn_translate(X5,rdn_neg(X2))
| ~ rdn_translate(X4,rdn_neg(X1))
| ~ rdn_translate(X3,rdn_pos(X0))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(cnf_transformation,[],[f744]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(cnf_transformation,[],[f753]) ).
tcf(c_376,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f781]) ).
tcf(c_403,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f808]) ).
tcf(c_453,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(cnf_transformation,[],[f858]) ).
tcf(c_4192,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n2),rdnn(X0))
| ~ rdn_positive_less(rdnn(n3),rdnn(X0)) ),
inference(superposition,[status(thm)],[c_316,c_323]) ).
tcf(c_4193,plain,
! [X0: $i] :
( rdn_positive_less(rdnn(n3),rdnn(X0))
| ~ rdn_positive_less(rdnn(n4),rdnn(X0)) ),
inference(superposition,[status(thm)],[c_317,c_323]) ).
tcf(c_4332,plain,
rdn_positive_less(rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_318,c_4193]) ).
tcf(c_4545,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(superposition,[status(thm)],[c_4332,c_4192]) ).
tcf(c_15194,plain,
! [X0: $i,X1: $i] :
( rdn_add_with_carry(rdnn(X0),rdnn(n2),rdnn(n3),rdnn(X1))
| ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(superposition,[status(thm)],[c_376,c_348]) ).
tcf(c_16357,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(superposition,[status(thm)],[c_403,c_15194]) ).
tcf(c_19785,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,X1)
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X2,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_16357,c_339]) ).
tcf(c_26690,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,X1)
| ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n3)))
| ~ rdn_translate(X2,rdn_neg(rdnn(n5))) ),
inference(global_subsumption_just,[status(thm)],[c_19785,c_4545,c_19785]) ).
tcf(c_26691,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X0,X2,X1)
| ~ rdn_translate(X2,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(renaming,[status(thm)],[c_26690]) ).
tcf(c_26701,plain,
! [X0: $i,X1: $i] :
( sum(X0,X1,nn3)
| ~ rdn_translate(X1,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_179,c_26691]) ).
tcf(c_33563,plain,
! [X0: $i] :
( sum(X0,nn5,nn3)
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(superposition,[status(thm)],[c_181,c_26701]) ).
tcf(c_35650,plain,
sum(n2,nn5,nn3),
inference(superposition,[status(thm)],[c_51,c_33563]) ).
tcf(c_35651,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_453,c_35650]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM316+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.43 % CPULimit : 300
% 0.09/15.43 % WCLimit : 300
% 0.09/15.43 % DateTime : Thu Sep 24 03:40:14 UTC 2026
% 0.09/15.44 % CPUTime :
% 0.09/15.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/15.48 Running first-order theorem proving
% 0.09/15.48 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/15.49
% 0.09/15.49 % ======== iProver multi-core TPTP/SMT =========
% 0.09/15.49
% 0.09/15.49 % Detected problem language: tptp
% 0.34/15.50 % Proving...
% 12.54/18.28 % SZS status Started for theBenchmark.p
% 12.54/18.28 % SZS status Theorem for theBenchmark.p
% 12.54/18.28
% 12.54/18.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.54/18.28
% 12.54/18.28 % ------ iProver source info
% 12.54/18.28
% 12.54/18.28 % git: date: 2026-07-19 20:42:38 +0200
% 12.54/18.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.54/18.28 % git: non_committed_changes: false
% 12.54/18.28
% 12.54/18.28 % ------ Parsing...
% 12.54/18.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 % ------ Problem Properties
% 12.54/18.28
% 12.54/18.28 %
% 12.54/18.28 % clauses 405
% 12.54/18.28 % conjectures 1
% 12.54/18.28 % EPR 11
% 12.54/18.28 % Horn 403
% 12.54/18.28 % unary 376
% 12.54/18.28 % binary 8
% 12.54/18.28 % lits 478
% 12.54/18.28 % lits eq 5
% 12.54/18.28 % fd_pure 0
% 12.54/18.28 % fd_pseudo 0
% 12.54/18.28 % fd_cond 0
% 12.54/18.28 % fd_pseudo_cond 5
% 12.54/18.28 % AC symbols 0
% 12.54/18.28
% 12.54/18.28 % ------ Input Options Time Limit: Unbounded
% 12.54/18.28
% 12.54/18.28
% 12.54/18.28 % ------
% 12.54/18.28 % Current options:
% 12.54/18.28 % ------
% 12.54/18.28
% 12.54/18.28
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % ------ Proving...
% 12.54/18.28 %
% 12.54/18.28
% 12.54/18.28 % SZS status Theorem for theBenchmark.p
% 12.54/18.28
% 12.54/18.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.54/18.28
% 12.54/18.28
%------------------------------------------------------------------------------