%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:27:19 PM UTC 2026
% Result : Theorem 15.59s 8.29s
% Output : CNFRefutation 15.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 30 unt; 0 def)
% Number of atoms : 52 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 9 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f83,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(f119,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f160,axiom,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_less__zeroE) ).
fof(f165,axiom,
! [X0] : number_number_of(int,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
fof(f206,axiom,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_less__0__number__of) ).
fof(f350,axiom,
! [X0] :
( zero_zero(nat) = number_number_of(nat,X0)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_eq__0__number__of) ).
fof(f375,axiom,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_power2__ge__self) ).
fof(f660,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f661,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f660]) ).
fof(f662,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(flattening,[],[f661]) ).
fof(f862,plain,
! [X0] :
( ( zero_zero(nat) != number_number_of(nat,X0)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| zero_zero(nat) = number_number_of(nat,X0) ) ),
inference(nnf_transformation,[],[f350]) ).
fof(f863,plain,
! [X0] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0))) ) ),
inference(nnf_transformation,[],[f206]) ).
fof(f941,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f662]) ).
fof(f1021,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(cnf_transformation,[],[f375]) ).
fof(f1100,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(cnf_transformation,[],[f83]) ).
fof(f1112,plain,
! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| zero_zero(nat) = number_number_of(nat,X0) ),
inference(cnf_transformation,[],[f862]) ).
fof(f1115,plain,
! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0))) ),
inference(cnf_transformation,[],[f863]) ).
fof(f1122,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f119]) ).
fof(f1190,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f160]) ).
fof(f1192,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f46]) ).
fof(f1228,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[],[f165]) ).
tcf(c_53,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(cnf_transformation,[],[f941]) ).
tcf(c_126,plain,
! [X0: $i] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(cnf_transformation,[],[f1021]) ).
tcf(c_203,plain,
number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int),
inference(cnf_transformation,[],[f1100]) ).
tcf(c_214,plain,
! [X0: $i] :
( ( number_number_of(nat,X0) = zero_zero(nat) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) ),
inference(cnf_transformation,[],[f1112]) ).
tcf(c_217,plain,
! [X0: $i] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) ),
inference(cnf_transformation,[],[f1115]) ).
tcf(c_224,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f1122]) ).
tcf(c_290,plain,
! [X0: $i] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f1190]) ).
tcf(c_292,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f1192]) ).
tcf(c_328,plain,
! [X0: $i] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[],[f1228]) ).
tcf(c_2904,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(demodulation,[status(thm)],[c_203,c_328]) ).
tcf(c_3160,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(light_normalisation,[status(thm)],[c_292,c_224]) ).
tcf(c_3236,plain,
! [X0: $i] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))),
inference(light_normalisation,[status(thm)],[c_126,c_2904]) ).
tcf(c_3433,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(light_normalisation,[status(thm)],[c_53,c_224,c_2904]) ).
tcf(c_18283,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),pls)),
inference(superposition,[status(thm)],[c_3433,c_3236]) ).
tcf(c_18341,plain,
number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(nat),
inference(superposition,[status(thm)],[c_18283,c_214]) ).
tcf(c_19845,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(superposition,[status(thm)],[c_18341,c_217]) ).
tcf(c_19850,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19845,c_290,c_3160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n008.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 05:44:14 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 15.59/8.29 % SZS status Started for theBenchmark.p
% 15.59/8.29 % SZS status Theorem for theBenchmark.p
% 15.59/8.29
% 15.59/8.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.59/8.29
% 15.59/8.29 % ------ iProver source info
% 15.59/8.29
% 15.59/8.29 % git: date: 2026-07-19 20:42:38 +0200
% 15.59/8.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.59/8.29 % git: non_committed_changes: false
% 15.59/8.29
% 15.59/8.29 % ------ Parsing...
% 15.59/8.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.59/8.29
% 15.59/8.29 % ------ Preprocessing... sup_sim: 79 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 21 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 15.59/8.29
% 15.59/8.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.59/8.29
% 15.59/8.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.59/8.29 % ------ Proving...
% 15.59/8.29 % ------ Problem Properties
% 15.59/8.29
% 15.59/8.29 %
% 15.59/8.29 % clauses 330
% 15.59/8.29 % conjectures 0
% 15.59/8.29 % EPR 0
% 15.59/8.29 % Horn 301
% 15.59/8.29 % unary 94
% 15.59/8.29 % binary 143
% 15.59/8.29 % lits 681
% 15.59/8.29 % lits eq 135
% 15.59/8.29 % fd_pure 0
% 15.59/8.29 % fd_pseudo 0
% 15.59/8.29 % fd_cond 15
% 15.59/8.29 % fd_pseudo_cond 16
% 15.59/8.29 % AC symbols 0
% 15.59/8.29
% 15.59/8.29 % ------ Schedule dynamic 5 is on
% 15.59/8.29
% 15.59/8.29 % ------ no conjectures: strip conj schedule
% 15.59/8.29
% 15.59/8.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 15.59/8.29
% 15.59/8.29
% 15.59/8.29 % ------
% 15.59/8.29 % Current options:
% 15.59/8.29 % ------
% 15.59/8.29
% 15.59/8.29
% 15.59/8.29 %
% 15.59/8.29
% 15.59/8.29 % ------ Proving...
% 15.59/8.29 %
% 15.59/8.29
% 15.59/8.29 % SZS status Theorem for theBenchmark.p
% 15.59/8.29
% 15.59/8.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.59/8.29
% 15.59/8.29
%------------------------------------------------------------------------------