%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM924+5 : TPTP v9.2.1. Released v5.3.0.
% 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 : n026.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 04:58:52 PM UTC 2026
% Result : Theorem 1.30s 1.71s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 18 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_97_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
fof(fact_22_number__of__is__id,axiom,
! [X14] : number_number_of(int,X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(fact_23_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_96_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
fof(fact_3_t,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(fact_62_mult__Pls,axiom,
! [X11] : times_times(int,pls,X11) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(c_0_8,negated_conjecture,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_9,negated_conjecture,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_10,plain,
zero_zero(int) = number_number_of(int,pls),
inference(split_conjunct,[status(thm)],[fact_97_zero__is__num__zero]) ).
fof(c_0_11,plain,
! [X402] : number_number_of(int,X402) = X402,
inference(variable_rename,[status(thm)],[fact_22_number__of__is__id]) ).
fof(c_0_12,plain,
! [X403,X404] : times_times(int,X403,X404) = times_times(int,X404,X403),
inference(variable_rename,[status(thm)],[fact_23_zmult__commute]) ).
fof(c_0_13,plain,
! [X551,X552] : plus_plus(int,X551,X552) = plus_plus(int,X552,X551),
inference(variable_rename,[status(thm)],[fact_96_zadd__commute]) ).
cnf(c_0_14,negated_conjecture,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),number_number_of(int,pls)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
cnf(c_0_17,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X482] : times_times(int,pls,X482) = pls,
inference(variable_rename,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_0_20,negated_conjecture,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),pls),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(split_conjunct,[status(thm)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
cnf(c_0_22,plain,
times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) = plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15]),c_0_17]),c_0_18]),c_0_17]),c_0_18]) ).
cnf(c_0_23,plain,
times_times(int,pls,X1) = pls,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(rw,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15]),c_0_17]),c_0_18]),c_0_17]),c_0_22]),c_0_15]),c_0_17]),c_0_18]),c_0_10]),c_0_15]),c_0_17]),c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM924+5 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 5 01:18:23 EDT 2026
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % start to proof: theBenchmark
% 1.30/1.71 % Version : CSE_E---1.7
% 1.30/1.71 % Problem : theBenchmark.p
% 1.30/1.71 % SZS status Theorem for theBenchmark.p
% 1.30/1.71 % SZS output start CNFRefutation
% See solution above
% 1.30/1.71 % Total time : 1.375s
%------------------------------------------------------------------------------