%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 1.15s 6.09s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 49 ( 8 unt; 4 def)
% Number of atoms : 122 ( 4 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 95 ( 39 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( less_or_equal(absolute(add(X0,X1)),X2)
| ~ less_or_equal(add(absolute(X0),absolute(X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
fof(f2,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).
fof(f3,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).
fof(f4,axiom,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).
fof(f5,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X2),X1)
| ~ less_or_equal(X2,half(X1))
| ~ less_or_equal(X0,half(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f8,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f9,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(f(X1),negate(f(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_1(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f10,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(g(X1),negate(g(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_2(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f11,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f12,axiom,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_1) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(absolute(add(X0,X1)),X2)
| ~ less_or_equal(add(absolute(X0),absolute(X1)),X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(X0,n0)
| ~ less_or_equal(minimum(X0,X1),n0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(add(X0,X2),X1)
| ~ less_or_equal(X2,half(X1))
| ~ less_or_equal(X0,half(X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(half(X0),n0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(delta_1(X0),n0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(delta_2(X0),n0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(f(X0),negate(f(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_1(X1)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(g(X0),negate(g(a_real_number)))),X1)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_2(X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_144,definition,
iPr_def_10 = f(a_real_number),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_145,definition,
iPr_def_11 = negate(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_146,definition,
iPr_def_12 = g(a_real_number),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_147,definition,
iPr_def_13 = negate(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_148,negated_conjecture,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(add(f(xs(X0)),iPr_def_11),add(g(xs(X0)),iPr_def_13))),epsilon_0) ),
inference(demodulation,[status(thm)],[c_74,c_146,c_147,c_144,c_145]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] :
( less_or_equal(minimum(X0,X1),n0)
| less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1) ),
inference(superposition,[status(thm)],[c_73,c_64]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i] :
( less_or_equal(minimum(X0,X1),n0)
| less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0) ),
inference(superposition,[status(thm)],[c_73,c_63]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(absolute(add(X0,X2)),X1)
| ~ less_or_equal(absolute(X2),half(X1))
| ~ less_or_equal(absolute(X0),half(X1)) ),
inference(superposition,[status(thm)],[c_66,c_62]) ).
tcf(c_469,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(g(xs(X0)),iPr_def_13)),half(epsilon_0))
| ~ less_or_equal(absolute(add(f(xs(X0)),iPr_def_11)),half(epsilon_0)) ),
inference(superposition,[status(thm)],[c_425,c_148]) ).
tcf(c_600,plain,
( less_or_equal(epsilon_0,n0)
| ~ less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_649,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(f(X0),iPr_def_11)),X1)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_1(X1)) ),
inference(light_normalisation,[status(thm)],[c_70,c_144,c_145]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(minimum(X0,delta_1(X1)),n0)
| less_or_equal(absolute(add(f(xs(minimum(X0,delta_1(X1)))),iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_406,c_649]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(absolute(add(g(X0),iPr_def_13)),X1)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_2(X1)) ),
inference(light_normalisation,[status(thm)],[c_71,c_146,c_147]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,n0)
| less_or_equal(minimum(delta_2(X0),X1),n0)
| less_or_equal(absolute(add(g(xs(minimum(delta_2(X0),X1))),iPr_def_13)),X0) ),
inference(superposition,[status(thm)],[c_407,c_716]) ).
tcf(c_894,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(delta_2(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_895,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1178,plain,
! [X0: $i] :
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(X0,delta_1(half(epsilon_0))),n0)
| ~ less_or_equal(absolute(add(g(xs(minimum(X0,delta_1(half(epsilon_0))))),iPr_def_13)),half(epsilon_0)) ),
inference(superposition,[status(thm)],[c_660,c_469]) ).
tcf(c_1520,plain,
! [X0: $i] :
( ~ less_or_equal(absolute(add(g(xs(minimum(X0,delta_1(half(epsilon_0))))),iPr_def_13)),half(epsilon_0))
| less_or_equal(minimum(X0,delta_1(half(epsilon_0))),n0) ),
inference(global_subsumption_just,[status(thm)],[c_1178,c_72,c_600,c_1178]) ).
tcf(c_1521,plain,
! [X0: $i] :
( less_or_equal(minimum(X0,delta_1(half(epsilon_0))),n0)
| ~ less_or_equal(absolute(add(g(xs(minimum(X0,delta_1(half(epsilon_0))))),iPr_def_13)),half(epsilon_0)) ),
inference(renaming,[status(thm)],[c_1520]) ).
tcf(c_1528,plain,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0) ),
inference(superposition,[status(thm)],[c_728,c_1521]) ).
tcf(c_1616,plain,
less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0),
inference(global_subsumption_just,[status(thm)],[c_1528,c_72,c_600,c_1528]) ).
tcf(c_1618,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(superposition,[status(thm)],[c_1616,c_65]) ).
tcf(c_1621,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1618,c_894,c_895,c_600,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 05:47:07 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 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
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.45 % Proving...
% 1.15/6.09 % SZS status Started for theBenchmark.p
% 1.15/6.09 % SZS status Unsatisfiable for theBenchmark.p
% 1.15/6.09
% 1.15/6.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.15/6.09
% 1.15/6.09 % ------ iProver source info
% 1.15/6.09
% 1.15/6.09 % git: date: 2026-07-19 20:42:38 +0200
% 1.15/6.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.15/6.09 % git: non_committed_changes: false
% 1.15/6.09
% 1.15/6.09 % ------ Parsing...% successful
% 1.15/6.09
% 1.15/6.09
% 1.15/6.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.15/6.09
% 1.15/6.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.15/6.09
% 1.15/6.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.15/6.09
% 1.15/6.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.15/6.09 % ------ Proving...
% 1.15/6.09 % ------ Problem Properties
% 1.15/6.09
% 1.15/6.09 %
% 1.15/6.09 % clauses 17
% 1.15/6.09 % conjectures 1
% 1.15/6.09 % EPR 1
% 1.15/6.09 % Horn 13
% 1.15/6.09 % unary 5
% 1.15/6.09 % binary 8
% 1.15/6.09 % lits 33
% 1.15/6.09 % lits eq 4
% 1.15/6.09 % fd_pure 0
% 1.15/6.09 % fd_pseudo 0
% 1.15/6.09 % fd_cond 0
% 1.15/6.09 % fd_pseudo_cond 0
% 1.15/6.09 % AC symbols 0
% 1.15/6.09
% 1.15/6.09 % ------ Schedule dynamic 5 is on
% 1.15/6.09
% 1.15/6.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.15/6.09
% 1.15/6.09
% 1.15/6.09 % ------
% 1.15/6.09 % Current options:
% 1.15/6.09 % ------
% 1.15/6.09
% 1.15/6.09
% 1.15/6.09 %
% 1.15/6.09
% 1.15/6.09 % ------ Proving...
% 1.15/6.09 %
% 1.15/6.09
% 1.15/6.09 % SZS status Unsatisfiable for theBenchmark.p
% 1.15/6.09
% 1.15/6.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.15/6.09
% 1.15/6.09
%------------------------------------------------------------------------------