%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 12:55:34 PM UTC 2026
% Result : Unsatisfiable 28.30s 9.84s
% Output : CNFRefutation 28.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 10 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 202 ( 93 ~; 109 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than_or_equal(X1,X0)
| less_than_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_less) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f4,axiom,
! [X0,X1] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,q(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation1) ).
fof(f5,axiom,
! [X0,X1] :
( less_than_or_equal(X1,X0)
| ~ less_than_or_equal(q(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation2) ).
fof(f6,axiom,
! [X0] :
( ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,h(X0))
| less_than_or_equal(f(X0),n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
fof(f7,axiom,
! [X0,X1] :
( ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(lower_bound,X0)
| 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/sandbox/benchmark/theBenchmark.p',continuity2) ).
fof(f8,axiom,
! [X0] :
( ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(k(X0),X0)
| less_than_or_equal(n0,f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity3) ).
fof(f9,axiom,
! [X0,X1] :
( ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(lower_bound,X0)
| 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/sandbox/benchmark/theBenchmark.p',continuity4) ).
fof(f10,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/sandbox/benchmark/theBenchmark.p',crossover1) ).
fof(f11,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(g(X0),upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
fof(f12,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(f(g(X0)),n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
fof(f13,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(g(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
fof(f14,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_interval) ).
fof(f15,axiom,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_mapping) ).
fof(f16,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_mapping) ).
fof(f17,negated_conjecture,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X1,X0)
| less_than_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,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,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,q(X1,X0)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( less_than_or_equal(X1,X0)
| ~ less_than_or_equal(q(X0,X1),X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,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(cnf_transformation,[],[f6]) ).
tcf(c_72,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(cnf_transformation,[],[f7]) ).
tcf(c_73,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(cnf_transformation,[],[f8]) ).
tcf(c_74,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(cnf_transformation,[],[f9]) ).
tcf(c_75,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,[],[f10]) ).
tcf(c_76,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| less_than_or_equal(g(X0),upper_bound) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| less_than_or_equal(f(g(X0)),n0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(g(X0),X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_79,plain,
less_than_or_equal(lower_bound,upper_bound),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,plain,
less_than_or_equal(f(lower_bound),n0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,plain,
less_than_or_equal(n0,f(upper_bound)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,negated_conjecture,
( ~ less_than_or_equal(n0,f(l))
| ~ less_than_or_equal(f(l),n0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_198,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_75]) ).
tcf(c_210,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_73]) ).
tcf(c_276,plain,
( less_than_or_equal(l,h(l))
| ~ less_than_or_equal(g(h(l)),h(l)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_277,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(f(g(h(l))),n0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_278,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(g(h(l)),upper_bound) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_279,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_72]) ).
tcf(c_312,plain,
( less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(g(upper_bound),upper_bound) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_314,plain,
( less_than_or_equal(l,upper_bound)
| less_than_or_equal(g(upper_bound),upper_bound) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_320,plain,
! [X0: $i] :
( less_than_or_equal(n0,f(l))
| less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,X0)
| ~ less_than_or_equal(n0,f(X0)) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_362,plain,
( less_than_or_equal(k(l),l)
| ~ less_than_or_equal(k(l),q(l,k(l))) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_363,plain,
( less_than_or_equal(k(l),l)
| ~ less_than_or_equal(q(l,k(l)),l) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_484,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_75]) ).
tcf(c_838,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_320]) ).
tcf(c_1272,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_279]) ).
tcf(c_1346,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,h(l))
| ~ less_than_or_equal(n0,f(l)) ),
inference(resolution,[status(thm)],[c_82,c_71]) ).
tcf(c_1347,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(n0,f(l)) ),
inference(global_subsumption_just,[status(thm)],[c_1346,c_79,c_80,c_82,c_198,c_278,c_277,c_276,c_314,c_312,c_484,c_1272,c_1346]) ).
tcf(c_1349,plain,
~ less_than_or_equal(n0,f(l)),
inference(global_subsumption_just,[status(thm)],[c_1347,c_314,c_312,c_1347]) ).
tcf(c_1554,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(k(l),l) ),
inference(resolution,[status(thm)],[c_1349,c_73]) ).
tcf(c_1555,plain,
~ less_than_or_equal(k(l),l),
inference(global_subsumption_just,[status(thm)],[c_1554,c_79,c_80,c_198,c_210,c_314,c_312,c_1347]) ).
tcf(c_1676,plain,
! [X0: $i] :
( less_than_or_equal(upper_bound,X0)
| less_than_or_equal(X0,upper_bound) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1840,plain,
! [X0: $i] :
( less_than_or_equal(l,X0)
| less_than_or_equal(X0,l) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_2087,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_68]) ).
tcf(c_2089,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_74]) ).
tcf(c_2578,plain,
less_than_or_equal(l,upper_bound),
inference(superposition,[status(thm)],[c_76,c_78]) ).
tcf(c_3204,plain,
( less_than_or_equal(l,q(l,k(l)))
| less_than_or_equal(q(l,k(l)),l) ),
inference(instantiation,[status(thm)],[c_1840]) ).
tcf(c_3208,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_2087]) ).
tcf(c_3209,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_1676]) ).
tcf(c_3565,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_67]) ).
tcf(c_9041,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_75]) ).
tcf(c_9042,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9041,c_3565,c_3209,c_3208,c_3204,c_2578,c_2089,c_1555,c_1349,c_838,c_363,c_362,c_198,c_80,c_81,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 05:42:56 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 28.30/9.84 % SZS status Started for theBenchmark.p
% 28.30/9.84 % SZS status Unsatisfiable for theBenchmark.p
% 28.30/9.84
% 28.30/9.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.30/9.84
% 28.30/9.84 % ------ iProver source info
% 28.30/9.84
% 28.30/9.84 % git: date: 2026-07-19 20:42:38 +0200
% 28.30/9.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.30/9.84 % git: non_committed_changes: false
% 28.30/9.84
% 28.30/9.84 % ------ Parsing...% successful
% 28.30/9.84
% 28.30/9.84
% 28.30/9.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 28.30/9.84
% 28.30/9.84 % ------ Preprocessing...%
% 28.30/9.84
% 28.30/9.84 % ------ Preprocessing...
% 28.30/9.84 % ------ Proving...
% 28.30/9.84 % ------ Problem Properties
% 28.30/9.84
% 28.30/9.84 %
% 28.30/9.84 % clauses 17
% 28.30/9.84 % conjectures 1
% 28.30/9.84 % EPR 4
% 28.30/9.84 % Horn 12
% 28.30/9.84 % unary 4
% 28.30/9.84 % binary 7
% 28.30/9.84 % lits 44
% 28.30/9.84 % lits eq 0
% 28.30/9.84 % fd_pure 0
% 28.30/9.84 % fd_pseudo 0
% 28.30/9.84 % fd_cond 0
% 28.30/9.84 % fd_pseudo_cond 0
% 28.30/9.84 % AC symbols 0
% 28.30/9.84
% 28.30/9.84 % ------ Input Options Time Limit: Unbounded
% 28.30/9.84
% 28.30/9.84
% 28.30/9.84 % ------
% 28.30/9.84 % Current options:
% 28.30/9.84 % ------
% 28.30/9.84
% 28.30/9.84
% 28.30/9.84 %
% 28.30/9.84
% 28.30/9.84 % ------ Proving...
% 28.30/9.84 %
% 28.30/9.84
% 28.30/9.84 % SZS status Unsatisfiable for theBenchmark.p
% 28.30/9.84
% 28.30/9.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.30/9.84
% 28.30/9.84
%------------------------------------------------------------------------------