%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM294+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 : 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 04:53:05 PM UTC 2026
% Result : Theorem 75.46s 41.59s
% Output : CNFRefutation 75.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 15 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_entry_point_pos_pos,axiom,
! [X1,X2,X10,X11] :
( ( rdn_translate(X1,rdn_pos(X10))
& rdn_translate(X2,rdn_pos(X11))
& rdn_positive_less(X10,X11) )
=> less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(n12_less_something,conjecture,
? [X1] : less(n12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n12_less_something) ).
fof(rdn13,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn13) ).
fof(rdn_positive_less_multi_digit_low,axiom,
! [X4,X8,X6] :
( ( rdn_positive_less(rdnn(X4),rdnn(X6))
& rdn_non_zero(X8) )
=> rdn_positive_less(rdn(rdnn(X4),X8),rdn(rdnn(X6),X8)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_multi_digit_low) ).
fof(rdn_non_zero_by_digit,axiom,
! [X1] :
( rdn_non_zero_digit(rdnn(X1))
=> rdn_non_zero(rdnn(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_non_zero_by_digit) ).
fof(rdn12,axiom,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn12) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(rdn_digit1,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_digit1) ).
fof(c_0_8,plain,
! [X171,X172,X173,X174] :
( ~ rdn_translate(X171,rdn_pos(X173))
| ~ rdn_translate(X172,rdn_pos(X174))
| ~ rdn_positive_less(X173,X174)
| less(X171,X172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])]) ).
fof(c_0_9,negated_conjecture,
~ ? [X1] : less(n12,X1),
inference(assume_negation,[status(cth)],[n12_less_something]) ).
cnf(c_0_10,plain,
( less(X1,X3)
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ rdn_positive_less(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(split_conjunct,[status(thm)],[rdn13]) ).
fof(c_0_12,negated_conjecture,
! [X276] : ~ less(n12,X276),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_13,plain,
! [X162,X163,X164] :
( ~ rdn_positive_less(rdnn(X162),rdnn(X164))
| ~ rdn_non_zero(X163)
| rdn_positive_less(rdn(rdnn(X162),X163),rdn(rdnn(X164),X163)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_multi_digit_low])]) ).
fof(c_0_14,plain,
! [X168] :
( ~ rdn_non_zero_digit(rdnn(X168))
| rdn_non_zero(rdnn(X168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_non_zero_by_digit])]) ).
cnf(c_0_15,plain,
( less(X1,n13)
| ~ rdn_positive_less(X2,rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(split_conjunct,[status(thm)],[rdn12]) ).
cnf(c_0_17,negated_conjecture,
~ less(n12,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( rdn_positive_less(rdn(rdnn(X1),X3),rdn(rdnn(X2),X3))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_non_zero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_20,plain,
( rdn_non_zero(rdnn(X1))
| ~ rdn_non_zero_digit(rdnn(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(split_conjunct,[status(thm)],[rdn_digit1]) ).
cnf(c_0_22,plain,
~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n3),rdnn(n1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
( rdn_positive_less(rdn(rdnn(n2),X1),rdn(rdnn(n3),X1))
| ~ rdn_non_zero(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
rdn_non_zero(rdnn(n1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM294+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 00:24:31 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 75.46/41.59 % Version : CSE_E---1.7
% 75.46/41.59 % Problem : theBenchmark.p
% 75.46/41.59 % SZS status Theorem for theBenchmark.p
% 75.46/41.59 % SZS output start CNFRefutation
% See solution above
% 75.56/41.64 % Total time : 39.687s
%------------------------------------------------------------------------------