%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA002-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 12:55:33 PM UTC 2026
% Result : Unsatisfiable 17.40s 3.30s
% Output : CNFRefutation 17.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 17
% Syntax : Number of formulae : 64 ( 10 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 210 ( 95 ~; 115 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X0,X1)
| in_interval(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_interval) ).
fof(f3,axiom,
! [X0,X1] :
( less_than_or_equal(X1,X0)
| less_than_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_less) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ less_than_or_equal(X2,X1)
| ~ less_than_or_equal(X0,X2)
| less_than_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f5,axiom,
! [X0,X1] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,q(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation1) ).
fof(f6,axiom,
! [X0,X1] :
( less_than_or_equal(X1,X0)
| ~ less_than_or_equal(q(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation2) ).
fof(f7,axiom,
! [X0] :
( ~ in_interval(lower_bound,X0,upper_bound)
| ~ less_than_or_equal(X0,h(X0))
| less_than_or_equal(f(X0),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ in_interval(lower_bound,X0,upper_bound)
| less_than_or_equal(X1,h(X0))
| ~ less_than_or_equal(f(X1),n0)
| ~ less_than_or_equal(X1,X0)
| less_than_or_equal(f(X0),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
fof(f9,axiom,
! [X0] :
( ~ in_interval(lower_bound,X0,upper_bound)
| ~ less_than_or_equal(k(X0),X0)
| less_than_or_equal(n0,f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity3) ).
fof(f10,axiom,
! [X0,X1] :
( ~ in_interval(lower_bound,X0,upper_bound)
| less_than_or_equal(k(X0),X1)
| ~ less_than_or_equal(n0,f(X1))
| ~ less_than_or_equal(X0,X1)
| less_than_or_equal(n0,f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity4) ).
fof(f11,axiom,
! [X0] :
( ~ less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,upper_bound)
| less_than_or_equal(X0,l) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover1) ).
fof(f12,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(g(X0),upper_bound) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
fof(f13,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(f(g(X0)),n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
fof(f14,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(g(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
fof(f15,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_interval) ).
fof(f16,axiom,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_mapping) ).
fof(f17,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_mapping) ).
fof(f18,negated_conjecture,
~ in_interval(f(l),n0,f(l)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_interval(X0,X1,X2)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X1,X0)
| less_than_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than_or_equal(X0,X2)
| ~ less_than_or_equal(X1,X2)
| ~ less_than_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,q(X1,X0)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X1,X0)
| ~ less_than_or_equal(q(X0,X1),X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,plain,
! [X0: $i] :
( less_than_or_equal(f(X0),n0)
| ~ in_interval(lower_bound,X0,upper_bound)
| ~ less_than_or_equal(X0,h(X0)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(f(X0),n0)
| less_than_or_equal(X1,h(X0))
| ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(f(X1),n0)
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_75,plain,
! [X0: $i] :
( less_than_or_equal(n0,f(X0))
| ~ in_interval(lower_bound,X0,upper_bound)
| ~ less_than_or_equal(k(X0),X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(n0,f(X0))
| less_than_or_equal(k(X0),X1)
| ~ less_than_or_equal(X0,X1)
| ~ less_than_or_equal(n0,f(X1))
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_77,plain,
! [X0: $i] :
( less_than_or_equal(X0,l)
| ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(f(X0),n0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_78,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| less_than_or_equal(g(X0),upper_bound) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_79,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| less_than_or_equal(f(g(X0)),n0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(g(X0),X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_81,plain,
less_than_or_equal(lower_bound,upper_bound),
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,plain,
less_than_or_equal(f(lower_bound),n0),
inference(cnf_transformation,[],[f16]) ).
tcf(c_83,plain,
less_than_or_equal(n0,f(upper_bound)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_84,negated_conjecture,
~ in_interval(f(l),n0,f(l)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X1),X0)
| ~ less_than_or_equal(lower_bound,X1)
| ~ less_than_or_equal(X1,upper_bound)
| ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(n0,f(X0)) ),
inference(resolution,[status(thm)],[c_67,c_76]) ).
tcf(c_196,plain,
! [X0: $i] :
( less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(k(X0),X0) ),
inference(resolution,[status(thm)],[c_67,c_75]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(f(X1),n0)
| less_than_or_equal(X0,h(X1))
| ~ less_than_or_equal(lower_bound,X1)
| ~ less_than_or_equal(X1,upper_bound)
| ~ less_than_or_equal(X0,X1)
| ~ less_than_or_equal(f(X0),n0) ),
inference(resolution,[status(thm)],[c_67,c_74]) ).
tcf(c_229,plain,
! [X0: $i] :
( less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(X0,h(X0)) ),
inference(resolution,[status(thm)],[c_67,c_73]) ).
tcf(c_243,plain,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
inference(resolution,[status(thm)],[c_67,c_84]) ).
tcf(c_392,plain,
( less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(lower_bound,upper_bound)
| ~ less_than_or_equal(f(lower_bound),n0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_393,plain,
! [X0: $i] :
( less_than_or_equal(n0,f(X0))
| less_than_or_equal(k(X0),upper_bound)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(n0,f(upper_bound)) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_397,plain,
( less_than_or_equal(f(l),n0)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,h(l)) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_398,plain,
( less_than_or_equal(l,h(l))
| ~ less_than_or_equal(g(h(l)),h(l)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_399,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(f(g(h(l))),n0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_400,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(g(h(l)),upper_bound) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_402,plain,
( less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(k(l),l) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_415,plain,
! [X0: $i] :
( less_than_or_equal(k(X0),X0)
| ~ less_than_or_equal(k(X0),q(X0,k(X0))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_420,plain,
! [X0: $i] :
( less_than_or_equal(k(X0),X0)
| ~ less_than_or_equal(q(X0,k(X0)),X0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_423,plain,
( less_than_or_equal(n0,f(l))
| less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(n0,f(upper_bound)) ),
inference(instantiation,[status(thm)],[c_393]) ).
tcf(c_479,plain,
! [X0: $i] :
( less_than_or_equal(f(l),n0)
| less_than_or_equal(X0,h(l))
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(X0,l)
| ~ less_than_or_equal(f(X0),n0) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_556,plain,
( less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(g(h(l)),upper_bound)
| ~ less_than_or_equal(f(g(h(l))),n0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_679,plain,
( less_than_or_equal(k(l),l)
| ~ less_than_or_equal(q(l,k(l)),l) ),
inference(instantiation,[status(thm)],[c_420]) ).
tcf(c_680,plain,
( less_than_or_equal(k(l),l)
| ~ less_than_or_equal(k(l),q(l,k(l))) ),
inference(instantiation,[status(thm)],[c_415]) ).
tcf(c_722,plain,
( less_than_or_equal(f(l),n0)
| less_than_or_equal(g(h(l)),h(l))
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(f(g(h(l))),n0) ),
inference(instantiation,[status(thm)],[c_479]) ).
tcf(c_806,plain,
! [X0: $i] :
( less_than_or_equal(upper_bound,X0)
| less_than_or_equal(X0,upper_bound) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1298,plain,
! [X0: $i] :
( less_than_or_equal(k(l),q(l,k(l)))
| ~ less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(X0,q(l,k(l))) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1300,plain,
( less_than_or_equal(n0,f(l))
| less_than_or_equal(k(l),q(l,k(l)))
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,q(l,k(l)))
| ~ less_than_or_equal(n0,f(q(l,k(l)))) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_1303,plain,
( less_than_or_equal(l,q(l,k(l)))
| less_than_or_equal(q(l,k(l)),l) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1306,plain,
( less_than_or_equal(q(l,k(l)),l)
| ~ less_than_or_equal(q(l,k(l)),upper_bound)
| ~ less_than_or_equal(f(q(l,k(l))),n0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_2555,plain,
less_than_or_equal(l,upper_bound),
inference(superposition,[status(thm)],[c_78,c_80]) ).
tcf(c_3456,plain,
( less_than_or_equal(n0,f(q(l,k(l))))
| less_than_or_equal(f(q(l,k(l))),n0) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_3490,plain,
( less_than_or_equal(upper_bound,q(l,k(l)))
| less_than_or_equal(q(l,k(l)),upper_bound) ),
inference(instantiation,[status(thm)],[c_806]) ).
tcf(c_4007,plain,
( less_than_or_equal(k(l),q(l,k(l)))
| ~ less_than_or_equal(k(l),upper_bound)
| ~ less_than_or_equal(upper_bound,q(l,k(l))) ),
inference(instantiation,[status(thm)],[c_1298]) ).
tcf(c_4008,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4007,c_3490,c_3456,c_2555,c_1306,c_1303,c_1300,c_722,c_679,c_680,c_556,c_423,c_402,c_398,c_399,c_400,c_397,c_392,c_243,c_82,c_83,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA002-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 05:40:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 17.40/3.30 % SZS status Started for theBenchmark.p
% 17.40/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 17.40/3.30
% 17.40/3.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.40/3.30
% 17.40/3.30 % ------ iProver source info
% 17.40/3.30
% 17.40/3.30 % git: date: 2026-07-19 20:42:38 +0200
% 17.40/3.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.40/3.30 % git: non_committed_changes: false
% 17.40/3.30
% 17.40/3.30 % ------ Parsing...% successful
% 17.40/3.30
% 17.40/3.30
% 17.40/3.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.40/3.30
% 17.40/3.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 17.40/3.30
% 17.40/3.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.40/3.30 % ------ Proving...
% 17.40/3.30 % ------ Problem Properties
% 17.40/3.30
% 17.40/3.30 %
% 17.40/3.30 % clauses 17
% 17.40/3.30 % conjectures 0
% 17.40/3.30 % EPR 4
% 17.40/3.30 % Horn 12
% 17.40/3.30 % unary 4
% 17.40/3.30 % binary 7
% 17.40/3.30 % lits 44
% 17.40/3.30 % lits eq 0
% 17.40/3.30 % fd_pure 0
% 17.40/3.30 % fd_pseudo 0
% 17.40/3.30 % fd_cond 0
% 17.40/3.30 % fd_pseudo_cond 0
% 17.40/3.30 % AC symbols 0
% 17.40/3.30
% 17.40/3.30 % ------ Input Options Time Limit: Unbounded
% 17.40/3.30
% 17.40/3.30
% 17.40/3.30 % ------
% 17.40/3.30 % Current options:
% 17.40/3.30 % ------
% 17.40/3.30
% 17.40/3.30
% 17.40/3.30 %
% 17.40/3.30
% 17.40/3.30 % ------ Proving...
% 17.40/3.30 %
% 17.40/3.30
% 17.40/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 17.40/3.30
% 17.40/3.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.40/3.30
% 17.40/3.30
%------------------------------------------------------------------------------