%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM325+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 : n012.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 04:53:10 PM UTC 2026
% Result : Theorem 207.33s 59.60s
% Output : CNFRefutation 207.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 24 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 68 ( 32 ~; 27 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 56 ( 2 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn_positive_less_transitivity,axiom,
! [X1,X2,X3] :
( ( rdn_positive_less(rdnn(X1),rdnn(X2))
& rdn_positive_less(rdnn(X2),rdnn(X3)) )
=> rdn_positive_less(rdnn(X1),rdnn(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(sum_entry_point_pos_neg_2,axiom,
! [X1,X2,X3,X10,X11,X12] :
( ( rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X2,rdn_neg(X11))
& rdn_positive_less(X11,X10)
& rdn_add_with_carry(rdnn(n0),X11,X12,X10)
& rdn_translate(X3,rdn_pos(X12)) )
=> sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_2) ).
fof(sum_what_nn2_n3,conjecture,
? [X1] : sum(X1,nn2,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_what_nn2_n3) ).
fof(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(rdn_positive_less45,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
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(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
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(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
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(c_0_12,plain,
! [X155,X156,X157] :
( ~ rdn_positive_less(rdnn(X155),rdnn(X156))
| ~ rdn_positive_less(rdnn(X156),rdnn(X157))
| rdn_positive_less(rdnn(X155),rdnn(X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_transitivity])]) ).
fof(c_0_13,plain,
! [X208,X209,X210,X211,X212,X213] :
( ~ rdn_translate(X208,rdn_pos(X211))
| ~ rdn_translate(X209,rdn_neg(X212))
| ~ rdn_positive_less(X212,X211)
| ~ rdn_add_with_carry(rdnn(n0),X212,X213,X211)
| ~ rdn_translate(X210,rdn_pos(X213))
| sum(X208,X209,X210) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_neg_2])]) ).
fof(c_0_14,negated_conjecture,
~ ? [X1] : sum(X1,nn2,n3),
inference(assume_negation,[status(cth)],[sum_what_nn2_n3]) ).
cnf(c_0_15,plain,
( rdn_positive_less(rdnn(X1),rdnn(X3))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X2),rdnn(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(split_conjunct,[status(thm)],[rdn_positive_less34]) ).
cnf(c_0_17,plain,
( sum(X1,X3,X6)
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_neg(X4))
| ~ rdn_positive_less(X4,X2)
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X2)
| ~ rdn_translate(X6,rdn_pos(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
fof(c_0_19,negated_conjecture,
! [X276] : ~ sum(X276,nn2,n3),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_20,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(split_conjunct,[status(thm)],[rdn_positive_less45]) ).
cnf(c_0_21,plain,
( rdn_positive_less(rdnn(X1),rdnn(n4))
| ~ rdn_positive_less(rdnn(X1),rdnn(n3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
fof(c_0_23,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])]) ).
cnf(c_0_24,plain,
( sum(X1,X2,n3)
| ~ rdn_add_with_carry(rdnn(n0),X3,rdnn(n3),X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_pos(X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdnn2]) ).
cnf(c_0_26,negated_conjecture,
~ sum(X1,nn2,n3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( rdn_positive_less(rdnn(X1),rdnn(n5))
| ~ rdn_positive_less(rdnn(X1),rdnn(n4)) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_28,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,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_23]) ).
cnf(c_0_30,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n0_n5_n0]) ).
cnf(c_0_31,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),X1)
| ~ rdn_positive_less(rdnn(n2),X1)
| ~ rdn_translate(X2,rdn_pos(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
cnf(c_0_33,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,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_29,c_0_30]) ).
cnf(c_0_35,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_36,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM325+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 00:26:16 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 207.33/59.60 % Version : CSE_E---1.7
% 207.33/59.60 % Problem : theBenchmark.p
% 207.33/59.60 % SZS status Theorem for theBenchmark.p
% 207.33/59.60 % SZS output start CNFRefutation
% See solution above
% 207.43/59.64 % Total time : 57.666s
%------------------------------------------------------------------------------