%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM313+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 : Tue May 5 04:53:08 PM UTC 2026
% Result : Theorem 210.65s 61.81s
% Output : CNFRefutation 210.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 65 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 23 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 56 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_entry_point_pos_pos,axiom,
! [X1,X2,X3,X10,X11,X12] :
( ( rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X2,rdn_pos(X11))
& rdn_add_with_carry(rdnn(n0),X10,X11,X12)
& rdn_translate(X3,rdn_pos(X12)) )
=> sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(add_digit_digit_digit,axiom,
! [X21,X22,X23,X24,X25] :
( ( rdn_digit_add(rdnn(X22),rdnn(X23),rdnn(X25),rdnn(n0))
& rdn_digit_add(rdnn(X25),rdnn(X21),rdnn(X24),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X21),rdnn(X22),rdnn(X23),rdnn(X24)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(sumn2_only_n3_n5,conjecture,
! [X1] :
( sum(n2,X1,n5)
=> X1 = n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sumn2_only_n3_n5) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(unique_RHS,axiom,
! [X1,X19,X20,X3] :
( ( sum(X1,X19,X3)
& sum(X1,X20,X3) )
=> X19 = X20 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',unique_RHS) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(rdn_digit_add_n2_n3_n5_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(c_0_9,plain,
! [X190,X191,X192,X193,X194,X195] :
( ~ rdn_translate(X190,rdn_pos(X193))
| ~ rdn_translate(X191,rdn_pos(X194))
| ~ rdn_add_with_carry(rdnn(n0),X193,X194,X195)
| ~ rdn_translate(X192,rdn_pos(X195))
| sum(X190,X191,X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])]) ).
fof(c_0_10,plain,
! [X237,X238,X239,X240,X241] :
( ~ rdn_digit_add(rdnn(X238),rdnn(X239),rdnn(X241),rdnn(n0))
| ~ rdn_digit_add(rdnn(X241),rdnn(X237),rdnn(X240),rdnn(n0))
| rdn_add_with_carry(rdnn(X237),rdnn(X238),rdnn(X239),rdnn(X240)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( sum(n2,X1,n5)
=> X1 = n3 ),
inference(assume_negation,[status(cth)],[sumn2_only_n3_n5]) ).
cnf(c_0_12,plain,
( sum(X1,X3,X6)
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X2,X4,X5)
| ~ rdn_translate(X6,rdn_pos(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
cnf(c_0_14,plain,
( rdn_add_with_carry(rdnn(X4),rdnn(X1),rdnn(X2),rdnn(X5))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X4),rdnn(X5),rdnn(n0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n0_n5_n0]) ).
fof(c_0_16,plain,
! [X230,X231,X232,X233] :
( ~ sum(X230,X231,X233)
| ~ sum(X230,X232,X233)
| X231 = X232 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unique_RHS])]) ).
fof(c_0_17,negated_conjecture,
( sum(n2,esk1_0,n5)
& esk1_0 != n3 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_18,plain,
( sum(X1,X2,n5)
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,rdnn(n5))
| ~ rdn_translate(X2,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
cnf(c_0_20,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n5))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n5),rdnn(n0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n2_n3_n5_n0]) ).
cnf(c_0_22,plain,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
sum(n2,esk1_0,n5),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( sum(X1,n3,n5)
| ~ rdn_add_with_carry(rdnn(n0),X2,rdnn(n3),rdnn(n5))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdn2]) ).
cnf(c_0_26,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( X1 = esk1_0
| ~ sum(n2,X1,n5) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
sum(n2,n3,n5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
esk1_0 != n3,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM313+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:26:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 210.65/61.81 % Version : CSE_E---1.7
% 210.65/61.81 % Problem : theBenchmark.p
% 210.65/61.81 % SZS status Theorem for theBenchmark.p
% 210.65/61.81 % SZS output start CNFRefutation
% See solution above
% 210.65/61.86 % Total time : 59.750s
%------------------------------------------------------------------------------