%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM303+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 : n023.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 04:53:07 PM UTC 2026
% Result : Theorem 35.22s 19.28s
% Output : CNFRefutation 35.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 49 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47 ( 22 ~; 15 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 4 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(n31_not_n12,conjecture,
n31 != n21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n31_not_n12) ).
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_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/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(rdn31,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn31) ).
fof(rdn_positive_less_multi_digit_high,axiom,
! [X4,X5,X6,X7] :
( rdn_positive_less(X5,X7)
=> rdn_positive_less(rdn(rdnn(X4),X5),rdn(rdnn(X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_multi_digit_high) ).
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(rdn21,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn21) ).
fof(c_0_7,negated_conjecture,
n31 = n21,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[n31_not_n12])]) ).
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,
! [X170,X171,X172,X173] :
( ~ rdn_translate(X170,rdn_pos(X172))
| ~ rdn_translate(X171,rdn_pos(X173))
| ~ rdn_positive_less(X172,X173)
| less(X170,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])]) ).
cnf(c_0_10,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(split_conjunct,[status(thm)],[rdn31]) ).
cnf(c_0_11,negated_conjecture,
n31 = n21,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,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_13,plain,
! [X157,X158,X159,X160] :
( ~ rdn_positive_less(X158,X160)
| rdn_positive_less(rdn(rdnn(X157),X158),rdn(rdnn(X159),X160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_multi_digit_high])]) ).
cnf(c_0_14,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_9]) ).
cnf(c_0_15,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X1 != X2
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( rdn_positive_less(rdn(rdnn(X3),X1),rdn(rdnn(X4),X2))
| ~ rdn_positive_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_19,plain,
( less(X1,n21)
| ~ rdn_positive_less(X2,rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(split_conjunct,[status(thm)],[rdn21]) ).
cnf(c_0_21,plain,
~ less(X1,X1),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
rdn_positive_less(rdn(rdnn(X1),rdnn(n2)),rdn(rdnn(X2),rdnn(n3))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM303+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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:26:38 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 35.22/19.28 % Version : CSE_E---1.7
% 35.22/19.28 % Problem : theBenchmark.p
% 35.22/19.28 % SZS status Theorem for theBenchmark.p
% 35.22/19.28 % SZS output start CNFRefutation
% See solution above
% 35.32/19.31 % Total time : 17.418s
%------------------------------------------------------------------------------