%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM344+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 04:53:14 PM UTC 2026
% Result : Theorem 55.28s 29.43s
% Output : CNFRefutation 55.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 24 ~; 21 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 51 ( 6 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_entry_point_neg_pos,axiom,
! [X1,X2,X3,X10,X11] :
( ( rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X2,rdn_pos(X11))
& sum(X2,X1,X3) )
=> sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_neg_pos) ).
fof(sum_entry_point_posx_negx,axiom,
! [X13,X14,X10] :
( ( rdn_translate(X13,rdn_pos(X10))
& rdn_translate(X14,rdn_neg(X10)) )
=> sum(X13,X14,n0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn1) ).
fof(rdnn1,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn1) ).
fof(less_entry_point_neg_pos,axiom,
! [X1,X2,X10,X11] :
( ( rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X2,rdn_pos(X11)) )
=> less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_pos) ).
fof(exist_bigger_plus_one,conjecture,
? [X1,X2] :
( sum(X1,n1,X2)
& less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(c_0_7,plain,
! [X218,X219,X220,X221,X222] :
( ~ rdn_translate(X218,rdn_neg(X221))
| ~ rdn_translate(X219,rdn_pos(X222))
| ~ sum(X219,X218,X220)
| sum(X218,X219,X220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_neg_pos])]) ).
fof(c_0_8,plain,
! [X215,X216,X217] :
( ~ rdn_translate(X215,rdn_pos(X217))
| ~ rdn_translate(X216,rdn_neg(X217))
| sum(X215,X216,n0) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_posx_negx])]) ).
cnf(c_0_9,plain,
( sum(X1,X3,X5)
| ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ sum(X3,X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(split_conjunct,[status(thm)],[rdn1]) ).
cnf(c_0_11,plain,
( sum(X1,X3,n0)
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_neg(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(split_conjunct,[status(thm)],[rdnn1]) ).
fof(c_0_13,plain,
! [X176,X177,X178,X179] :
( ~ rdn_translate(X176,rdn_neg(X178))
| ~ rdn_translate(X177,rdn_pos(X179))
| less(X176,X177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_neg_pos])]) ).
fof(c_0_14,negated_conjecture,
~ ? [X1,X2] :
( sum(X1,n1,X2)
& less(X1,X2) ),
inference(assume_negation,[status(cth)],[exist_bigger_plus_one]) ).
cnf(c_0_15,plain,
( sum(X1,n1,X2)
| ~ sum(n1,X1,X2)
| ~ rdn_translate(X1,rdn_neg(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( sum(X1,nn1,n0)
| ~ rdn_translate(X1,rdn_pos(rdnn(n1))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( less(X1,X3)
| ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X3,rdn_pos(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(split_conjunct,[status(thm)],[rdn0]) ).
fof(c_0_19,negated_conjecture,
! [X277,X278] :
( ~ sum(X277,n1,X278)
| ~ less(X277,X278) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_20,plain,
( sum(nn1,n1,X1)
| ~ sum(n1,nn1,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_21,plain,
sum(n1,nn1,n0),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,plain,
( less(X1,n0)
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ sum(X1,n1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
sum(nn1,n1,n0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
less(nn1,n0),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM344+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 00:28:18 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 55.28/29.43 % Version : CSE_E---1.7
% 55.28/29.43 % Problem : theBenchmark.p
% 55.28/29.43 % SZS status Theorem for theBenchmark.p
% 55.28/29.43 % SZS output start CNFRefutation
% See solution above
% 55.28/29.47 % Total time : 27.443s
%------------------------------------------------------------------------------