%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM925+3 : 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 : n026.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 02:27:18 PM UTC 2026
% Result : Theorem 1.30s 6.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 56 unt; 0 def)
% Number of atoms : 68 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 5 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f43,axiom,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__special_I3_J) ).
fof(f47,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
fof(f126,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
fof(f127,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f132,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f157,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f295,axiom,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_zero__less__power) ).
fof(f316,axiom,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_of__nat__less__0__iff) ).
fof(f322,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
fof(f372,axiom,
! [X0,X1,X2] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f378,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f795,axiom,
! [X0] : nat(number_number_of_int(X0)) = number_number_of_nat(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_nat__number__of) ).
fof(f1233,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1234,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f1233]) ).
fof(f1241,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f1234]) ).
fof(f1351,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
inference(ennf_transformation,[],[f295]) ).
fof(f2591,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f29]) ).
fof(f2611,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))),
inference(cnf_transformation,[],[f43]) ).
fof(f2615,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(cnf_transformation,[],[f47]) ).
fof(f2739,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f126]) ).
fof(f2740,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f127]) ).
fof(f2745,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f132]) ).
fof(f2776,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f157]) ).
fof(f2969,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X0))) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f3002,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f316]) ).
fof(f3008,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f322]) ).
fof(f3075,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f372]) ).
fof(f3081,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f378]) ).
fof(f3661,plain,
! [X0] : number_number_of_nat(X0) = nat(number_number_of_int(X0)),
inference(cnf_transformation,[],[f795]) ).
fof(f4364,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1241]) ).
fof(f4369,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f2591,f2740]) ).
fof(f4388,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,plus_plus_int(plus_plus_int(one_one_int,pls),pls))),
inference(definition_unfolding,[],[f2611,f2776]) ).
fof(f4392,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))),
inference(definition_unfolding,[],[f2615,f2745,f2776]) ).
fof(f4476,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f2739,f2745]) ).
fof(f4550,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X1),X0))) ),
inference(definition_unfolding,[],[f2969,f2740,f2740]) ).
fof(f4554,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f3002,f2740]) ).
fof(f4555,plain,
pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(definition_unfolding,[],[f3008,f2740]) ).
fof(f4988,plain,
pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(definition_unfolding,[],[f4364,f2740,f3661,f2745,f2776]) ).
tcf(c_77,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f4369]) ).
tcf(c_97,plain,
! [X0: $i] : number_number_of_int(plus_plus_int(X0,plus_plus_int(plus_plus_int(one_one_int,pls),pls))) = plus_plus_int(number_number_of_int(X0),one_one_int),
inference(cnf_transformation,[],[f4388]) ).
tcf(c_101,plain,
number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))) = plus_plus_int(one_one_int,one_one_int),
inference(cnf_transformation,[],[f4392]) ).
tcf(c_218,plain,
plus_plus_int(pls,pls) = pls,
inference(cnf_transformation,[],[f4476]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(power_power_int(X0),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(cnf_transformation,[],[f4550]) ).
tcf(c_465,plain,
! [X0: $i] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(cnf_transformation,[],[f4554]) ).
tcf(c_471,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls,
inference(cnf_transformation,[],[f4555]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X1,X2)),
inference(cnf_transformation,[],[f3075]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f3081]) ).
tcf(c_1760,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))) = pls,
inference(cnf_transformation,[],[f4988]) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i,X2: $i] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
inference(superposition,[status(thm)],[c_528,c_534]) ).
tcf(c_1943,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(superposition,[status(thm)],[c_471,c_465]) ).
tcf(c_2282,plain,
! [X0: $i] : number_number_of_int(plus_plus_int(X0,plus_plus_int(one_one_int,plus_plus_int(pls,pls)))) = plus_plus_int(one_one_int,number_number_of_int(X0)),
inference(demodulation,[status(thm)],[c_97,c_528,c_534]) ).
tcf(c_2283,plain,
! [X0: $i] : number_number_of_int(plus_plus_int(X0,plus_plus_int(one_one_int,pls))) = plus_plus_int(one_one_int,number_number_of_int(X0)),
inference(light_normalisation,[status(thm)],[c_2282,c_218]) ).
tcf(c_3251,plain,
number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls)))))) = plus_plus_int(one_one_int,one_one_int),
inference(demodulation,[status(thm)],[c_101,c_528,c_1806]) ).
tcf(c_3252,plain,
number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))) = plus_plus_int(one_one_int,one_one_int),
inference(light_normalisation,[status(thm)],[c_3251,c_218]) ).
tcf(c_3253,plain,
plus_plus_int(one_one_int,number_number_of_int(one_one_int)) = plus_plus_int(one_one_int,one_one_int),
inference(demodulation,[status(thm)],[c_3252,c_2283]) ).
tcf(c_4032,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls)))))))) = pls,
inference(demodulation,[status(thm)],[c_1760,c_528,c_1806]) ).
tcf(c_4033,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(one_one_int,plus_plus_int(one_one_int,pls))))) = pls,
inference(light_normalisation,[status(thm)],[c_4032,c_218]) ).
tcf(c_4034,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(plus_plus_int(one_one_int,number_number_of_int(one_one_int)))) = pls,
inference(demodulation,[status(thm)],[c_4033,c_2283]) ).
tcf(c_4035,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(plus_plus_int(one_one_int,one_one_int))) = pls,
inference(light_normalisation,[status(thm)],[c_4034,c_3253]) ).
tcf(c_4040,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(superposition,[status(thm)],[c_4035,c_435]) ).
tcf(c_4050,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4040,c_1943,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 05:45:43 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.30/6.74 % SZS status Started for theBenchmark.p
% 1.30/6.74 % SZS status Theorem for theBenchmark.p
% 1.30/6.74
% 1.30/6.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.30/6.74
% 1.30/6.74 % ------ iProver source info
% 1.30/6.74
% 1.30/6.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.30/6.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.30/6.74 % git: non_committed_changes: false
% 1.30/6.74
% 1.30/6.74 % ------ Parsing...
% 1.30/6.74 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.30/6.74 % ------ Proving...
% 1.30/6.74 % ------ Problem Properties
% 1.30/6.74
% 1.30/6.74 %
% 1.30/6.74 % clauses 1712
% 1.30/6.74 % conjectures 1
% 1.30/6.74 % EPR 41
% 1.30/6.74 % Horn 1520
% 1.30/6.74 % unary 544
% 1.30/6.74 % binary 599
% 1.30/6.74 % lits 3729
% 1.30/6.74 % lits eq 973
% 1.30/6.74 % fd_pure 0
% 1.30/6.74 % fd_pseudo 0
% 1.30/6.74 % fd_cond 110
% 1.30/6.74 % fd_pseudo_cond 95
% 1.30/6.74 % AC symbols 6
% 1.30/6.74
% 1.30/6.74 % ------ Input Options Time Limit: Unbounded
% 1.30/6.74
% 1.30/6.74
% 1.30/6.74 % ------
% 1.30/6.74 % Current options:
% 1.30/6.74 % ------
% 1.30/6.74
% 1.30/6.74
% 1.30/6.74 %
% 1.30/6.74
% 1.30/6.74 % ------ Proving...
% 1.30/6.74 %
% 1.30/6.74
% 1.30/6.74 % SZS status Theorem for theBenchmark.p
% 1.30/6.74
% 1.30/6.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.30/6.74
% 1.30/6.74
%------------------------------------------------------------------------------