%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM299+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 : n013.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 04:53:06 PM UTC 2026
% Result : Theorem 4.57s 3.23s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 55 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 55 ( 26 ~; 18 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_property,axiom,
! [X1,X2] :
( less(X1,X2)
<=> ( ~ less(X2,X1)
& X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_property) ).
fof(less_entry_point_neg_neg,axiom,
! [X1,X2,X10,X11] :
( ( rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X2,rdn_neg(X11))
& rdn_positive_less(X11,X10) )
=> less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_neg) ).
fof(nn2_not_less_nn4,conjecture,
~ less(nn2,nn4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nn2_not_less_nn4) ).
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(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
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(rdnn4,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn4) ).
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(c_0_8,plain,
! [X1,X2] :
( less(X1,X2)
<=> ( ~ less(X2,X1)
& X2 != X1 ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
fof(c_0_9,plain,
! [X178,X179,X180,X181] :
( ~ rdn_translate(X178,rdn_neg(X180))
| ~ rdn_translate(X179,rdn_neg(X181))
| ~ rdn_positive_less(X181,X180)
| less(X178,X179) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_neg_neg])]) ).
fof(c_0_10,plain,
! [X182,X183] :
( ( ~ less(X183,X182)
| ~ less(X182,X183) )
& ( X183 != X182
| ~ less(X182,X183) )
& ( less(X183,X182)
| X183 = X182
| less(X182,X183) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,negated_conjecture,
less(nn2,nn4),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nn2_not_less_nn4])]) ).
fof(c_0_12,plain,
! [X154,X155,X156] :
( ~ rdn_positive_less(rdnn(X154),rdnn(X155))
| ~ rdn_positive_less(rdnn(X155),rdnn(X156))
| rdn_positive_less(rdnn(X154),rdnn(X156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_transitivity])]) ).
cnf(c_0_13,plain,
( less(X1,X3)
| ~ rdn_translate(X1,rdn_neg(X2))
| ~ rdn_translate(X3,rdn_neg(X4))
| ~ rdn_positive_less(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdnn2]) ).
cnf(c_0_15,plain,
( ~ less(X1,X2)
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
less(nn2,nn4),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,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_18,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(split_conjunct,[status(thm)],[rdn_positive_less34]) ).
cnf(c_0_19,plain,
( less(X1,nn2)
| ~ rdn_positive_less(rdnn(n2),X2)
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(split_conjunct,[status(thm)],[rdnn4]) ).
cnf(c_0_21,negated_conjecture,
~ less(nn4,nn2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( rdn_positive_less(rdnn(X1),rdnn(n4))
| ~ rdn_positive_less(rdnn(X1),rdnn(n3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_24,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM299+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:25:56 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.57/3.23 % Version : CSE_E---1.7
% 4.57/3.23 % Problem : theBenchmark.p
% 4.57/3.23 % SZS status Theorem for theBenchmark.p
% 4.57/3.23 % SZS output start CNFRefutation
% See solution above
% 4.57/3.24 % Total time : 2.373s
%------------------------------------------------------------------------------