%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:27:15 PM UTC 2026
% Result : Theorem 3.47s 1.44s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 31 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 136 ( 136 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
one_one_int: int ).
tff(pred_def_1,type,
zprime: int > $o ).
tff(pred_def_2,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_3,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(pred_def_4,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(pred_def_5,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(pred_def_6,type,
twoSqu1431725154sum2sq: int > $o ).
tff(func_def_7,type,
zero_zero_nat: nat ).
tff(func_def_8,type,
bit0: int > int ).
tff(func_def_9,type,
bit1: int > int ).
tff(func_def_10,type,
pls: int ).
tff(func_def_11,type,
number_number_of_int: int > int ).
tff(func_def_12,type,
number_number_of_nat: int > nat ).
tff(func_def_13,type,
power_power_int: ( nat * int ) > int ).
tff(func_def_14,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_15,type,
m: int ).
tff(func_def_16,type,
s: int ).
tff(func_def_17,type,
t: int ).
tff(func_def_18,type,
sK0: int ).
tff(f3,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) ).
tff(f4,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) ).
tff(f25,axiom,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(f26,axiom,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(f31,axiom,
! [X0: int,X1: int,X2: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zmult__assoc) ).
tff(f66,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__1__add__1) ).
tff(f67,axiom,
! [X0: int] : ( times_times_int(pls,X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(f103,axiom,
! [X0: int,X1: int,X2: int] : ( plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_zadd__assoc) ).
tff(f105,axiom,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
tff(f106,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(f107,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) ).
tff(f108,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(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f108]) ).
tff(f185,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(cnf_transformation,[],[f3]) ).
tff(f186,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f211,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f25]) ).
tff(f212,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f219,plain,
! [X2: int,X0: int,X1: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tff(f276,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f66]) ).
tff(f277,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(cnf_transformation,[],[f67]) ).
tff(f335,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
tff(f337,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
tff(f338,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f106]) ).
tff(f339,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f109]) ).
tcf(c_51,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(cnf_transformation,[],[f185]) ).
tcf(c_52,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f186]) ).
tcf(c_77,plain,
! [X0_int: int] : number_number_of_int(X0_int) = X0_int,
inference(cnf_transformation,[],[f211]) ).
tcf(c_78,plain,
! [X0_int: int,X1_int: int] : times_times_int(X0_int,X1_int) = times_times_int(X1_int,X0_int),
inference(cnf_transformation,[],[f212]) ).
tcf(c_85,plain,
! [X0_int: int,X1_int: int,X2_int: int] : times_times_int(times_times_int(X0_int,X1_int),X2_int) = times_times_int(X0_int,times_times_int(X1_int,X2_int)),
inference(cnf_transformation,[],[f219]) ).
tcf(c_142,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f276]) ).
tcf(c_143,plain,
! [X0_int: int] : times_times_int(pls,X0_int) = pls,
inference(cnf_transformation,[],[f277]) ).
tcf(c_193,plain,
! [X0_int: int,X1_int: int,X2_int: int] : plus_plus_int(plus_plus_int(X0_int,X1_int),X2_int) = plus_plus_int(X0_int,plus_plus_int(X1_int,X2_int)),
inference(cnf_transformation,[],[f335]) ).
tcf(c_195,plain,
! [X0_int: int,X1_int: int] : plus_plus_int(X0_int,X1_int) = plus_plus_int(X1_int,X0_int),
inference(cnf_transformation,[],[f337]) ).
tcf(c_196,plain,
number_number_of_int(pls) = zero_zero_int,
inference(cnf_transformation,[],[f338]) ).
tcf(c_197,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(cnf_transformation,[],[f339]) ).
tcf(c_270,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))),times_times_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))))),
inference(theory_normalisation,[status(thm)],[c_51,c_85,c_78,c_193,c_195]) ).
tcf(c_271,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),
inference(theory_normalisation,[status(thm)],[c_52,c_85,c_78,c_193,c_195]) ).
tcf(c_277,negated_conjecture,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(theory_normalisation,[status(thm)],[c_197,c_85,c_78,c_193,c_195]) ).
tcf(c_1075,plain,
zero_zero_int = pls,
inference(demodulation,[status(thm)],[c_196,c_77]) ).
tcf(c_1295,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(light_normalisation,[status(thm)],[c_277,c_142,c_1075]) ).
tcf(c_1450,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(light_normalisation,[status(thm)],[c_271,c_142]) ).
tcf(c_1451,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,plus_plus_nat(one_one_nat,one_one_nat))),
inference(demodulation,[status(thm)],[c_1450,c_77]) ).
tcf(c_1466,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))))),
inference(light_normalisation,[status(thm)],[c_270,c_1075]) ).
tcf(c_1467,plain,
ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(demodulation,[status(thm)],[c_1466,c_77,c_143,c_1451]) ).
tcf(c_1468,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1467,c_1295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 05:36:00 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.54
% 0.24/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.54
% 0.24/0.54 % Detected problem language: tptp
% 0.24/0.56 % Proving...
% 3.47/1.44 % SZS status Started for theBenchmark.p
% 3.47/1.44 % SZS status Theorem for theBenchmark.p
% 3.47/1.44
% 3.47/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.47/1.44
% 3.47/1.44 % ------ iProver source info
% 3.47/1.44
% 3.47/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 3.47/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.47/1.44 % git: non_committed_changes: false
% 3.47/1.44
% 3.47/1.44 % ------ Parsing...
% 3.47/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.47/1.44 %
% 3.47/1.44
% 3.47/1.44 % ------ Preprocessing...%
% 3.47/1.44
% 3.47/1.44 % SZS status Theorem for theBenchmark.p
% 3.47/1.44
% 3.47/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.47/1.44
% 3.47/1.44
%------------------------------------------------------------------------------