%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM342+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 04:53:14 PM UTC 2026
% Result : Theorem 253.97s 63.94s
% Output : CNFRefutation 253.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 33 ~; 29 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 66 ( 0 sgn 30 !; 4 ?)
% 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/sandbox/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/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn8) ).
fof(rdn_digit_add_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(rdn_digit_add_n4_n0_n4_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n0_n4_n0) ).
fof(sum_and_difference,conjecture,
? [X1,X2] :
( sum(X1,X2,n8)
& difference(X1,X2,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_and_difference) ).
fof(rdn_digit_add_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(minus_entry_point,axiom,
! [X1,X2,X3] :
( sum(X2,X3,X1)
<=> difference(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',minus_entry_point) ).
fof(c_0_10,plain,
! [X191,X192,X193,X194,X195,X196] :
( ~ rdn_translate(X191,rdn_pos(X194))
| ~ rdn_translate(X192,rdn_pos(X195))
| ~ rdn_add_with_carry(rdnn(n0),X194,X195,X196)
| ~ rdn_translate(X193,rdn_pos(X196))
| sum(X191,X192,X193) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])]) ).
fof(c_0_11,plain,
! [X238,X239,X240,X241,X242] :
( ~ rdn_digit_add(rdnn(X239),rdnn(X240),rdnn(X242),rdnn(n0))
| ~ rdn_digit_add(rdnn(X242),rdnn(X238),rdnn(X241),rdnn(n0))
| rdn_add_with_carry(rdnn(X238),rdnn(X239),rdnn(X240),rdnn(X241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])]) ).
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_10]) ).
cnf(c_0_13,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(split_conjunct,[status(thm)],[rdn8]) ).
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_11]) ).
cnf(c_0_15,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(c_0_16,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(split_conjunct,[status(thm)],[rdn4]) ).
cnf(c_0_17,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n4_n0_n4_n0]) ).
fof(c_0_18,negated_conjecture,
~ ? [X1,X2] :
( sum(X1,X2,n8)
& difference(X1,X2,n0) ),
inference(assume_negation,[status(cth)],[sum_and_difference]) ).
cnf(c_0_19,plain,
( sum(X1,X2,n8)
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,rdnn(n8))
| ~ 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_20,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n8))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n8),rdnn(n0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(c_0_22,plain,
( sum(X1,X2,n4)
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,rdnn(n4))
| ~ rdn_translate(X2,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_23,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(split_conjunct,[status(thm)],[rdn0]) ).
cnf(c_0_24,plain,
( rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n4))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n4),rdnn(n0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
fof(c_0_25,negated_conjecture,
! [X277,X278] :
( ~ sum(X277,X278,n8)
| ~ difference(X277,X278,n0) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_26,plain,
( sum(X1,n4,n8)
| ~ rdn_add_with_carry(rdnn(n0),X2,rdnn(n4),rdnn(n8))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_27,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X235,X236,X237] :
( ( ~ sum(X236,X237,X235)
| difference(X235,X236,X237) )
& ( ~ difference(X235,X236,X237)
| sum(X236,X237,X235) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minus_entry_point])]) ).
cnf(c_0_29,plain,
( sum(X1,n0,n4)
| ~ rdn_add_with_carry(rdnn(n0),X2,rdnn(n0),rdnn(n4))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( ~ sum(X1,X2,n8)
| ~ difference(X1,X2,n0) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
sum(n4,n4,n8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_16]),c_0_27])]) ).
cnf(c_0_33,plain,
( difference(X3,X1,X2)
| ~ sum(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
sum(n4,n0,n4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
~ difference(n4,n4,n0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM342+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n025.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 00:27:43 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 253.97/63.94 % Version : CSE_E---1.7
% 253.97/63.94 % Problem : theBenchmark.p
% 253.97/63.94 % SZS status Theorem for theBenchmark.p
% 253.97/63.94 % SZS output start CNFRefutation
% See solution above
% 253.97/63.98 % Total time : 62.144s
%------------------------------------------------------------------------------