%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA003-4 : 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 : n018.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 1.34s 1.29s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 46 ( 8 unt; 4 def)
% Number of atoms : 115 ( 4 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 87 ( 35 ~; 52 |; 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 : 57 ( 0 sgn 57 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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(f3,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(f4,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(f5,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f8,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(f9,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(f10,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f11,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(f12,negated_conjecture,
! [X0] :
( ~ less_or_equal(add(absolute(add(f(xs(X0)),negate(f(a_real_number)))),absolute(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_2) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X0,minimum(X1,X2)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,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,[],[f3]) ).
tcf(c_64,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,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(half(X0),n0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(delta_1(X0),n0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(delta_2(X0),n0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,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,[],[f8]) ).
tcf(c_69,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,[],[f9]) ).
tcf(c_70,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] :
( less_or_equal(X0,n0)
| less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(add(absolute(add(f(xs(X0)),negate(f(a_real_number)))),absolute(add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_137,definition,
iPr_def_10 = f(a_real_number),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_138,definition,
iPr_def_11 = negate(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_139,definition,
iPr_def_12 = g(a_real_number),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_140,definition,
iPr_def_13 = negate(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_141,negated_conjecture,
! [X0: $i] :
( less_or_equal(X0,n0)
| ~ less_or_equal(add(absolute(add(f(xs(X0)),iPr_def_11)),absolute(add(g(xs(X0)),iPr_def_13))),epsilon_0) ),
inference(demodulation,[status(thm)],[c_72,c_139,c_140,c_137,c_138]) ).
tcf(c_387,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_71,c_62]) ).
tcf(c_388,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_71,c_61]) ).
tcf(c_408,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_64,c_141]) ).
tcf(c_559,plain,
( less_or_equal(epsilon_0,n0)
| ~ less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_585,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_68,c_137,c_138]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,n0)
| less_or_equal(minimum(delta_1(X0),X1),n0)
| less_or_equal(absolute(add(f(xs(minimum(delta_1(X0),X1))),iPr_def_11)),X0) ),
inference(superposition,[status(thm)],[c_388,c_585]) ).
tcf(c_754,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(delta_2(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_755,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_759,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_69,c_139,c_140]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,n0)
| less_or_equal(minimum(X0,delta_2(X1)),n0)
| less_or_equal(absolute(add(g(xs(minimum(X0,delta_2(X1)))),iPr_def_13)),X1) ),
inference(superposition,[status(thm)],[c_387,c_759]) ).
tcf(c_1124,plain,
! [X0: $i] :
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_1(half(epsilon_0)),X0),n0)
| ~ less_or_equal(absolute(add(g(xs(minimum(delta_1(half(epsilon_0)),X0))),iPr_def_13)),half(epsilon_0)) ),
inference(superposition,[status(thm)],[c_597,c_408]) ).
tcf(c_1190,plain,
! [X0: $i] :
( ~ less_or_equal(absolute(add(g(xs(minimum(delta_1(half(epsilon_0)),X0))),iPr_def_13)),half(epsilon_0))
| less_or_equal(minimum(delta_1(half(epsilon_0)),X0),n0) ),
inference(global_subsumption_just,[status(thm)],[c_1124,c_70,c_559,c_1124]) ).
tcf(c_1191,plain,
! [X0: $i] :
( less_or_equal(minimum(delta_1(half(epsilon_0)),X0),n0)
| ~ less_or_equal(absolute(add(g(xs(minimum(delta_1(half(epsilon_0)),X0))),iPr_def_13)),half(epsilon_0)) ),
inference(renaming,[status(thm)],[c_1190]) ).
tcf(c_1228,plain,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0) ),
inference(superposition,[status(thm)],[c_770,c_1191]) ).
tcf(c_1262,plain,
less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0),
inference(global_subsumption_just,[status(thm)],[c_1228,c_70,c_559,c_1228]) ).
tcf(c_1264,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(superposition,[status(thm)],[c_1262,c_63]) ).
tcf(c_1267,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1264,c_754,c_755,c_559,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:43:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.34/1.29 % SZS status Started for theBenchmark.p
% 1.34/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.29
% 1.34/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.34/1.29
% 1.34/1.29 % ------ iProver source info
% 1.34/1.29
% 1.34/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.34/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.34/1.29 % git: non_committed_changes: false
% 1.34/1.29
% 1.34/1.29 % ------ Parsing...% successful
% 1.34/1.29
% 1.34/1.29
% 1.34/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.34/1.29
% 1.34/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.34/1.29
% 1.34/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.34/1.29
% 1.34/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.34/1.29 % ------ Proving...
% 1.34/1.29 % ------ Problem Properties
% 1.34/1.29
% 1.34/1.29 %
% 1.34/1.29 % clauses 16
% 1.34/1.29 % conjectures 1
% 1.34/1.29 % EPR 1
% 1.34/1.29 % Horn 12
% 1.34/1.29 % unary 5
% 1.34/1.29 % binary 7
% 1.34/1.29 % lits 31
% 1.34/1.29 % lits eq 4
% 1.34/1.29 % fd_pure 0
% 1.34/1.29 % fd_pseudo 0
% 1.34/1.29 % fd_cond 0
% 1.34/1.29 % fd_pseudo_cond 0
% 1.34/1.29 % AC symbols 0
% 1.34/1.29
% 1.34/1.29 % ------ Schedule dynamic 5 is on
% 1.34/1.29
% 1.34/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.34/1.29
% 1.34/1.29
% 1.34/1.29 % ------
% 1.34/1.29 % Current options:
% 1.34/1.29 % ------
% 1.34/1.29
% 1.34/1.29
% 1.34/1.29 %
% 1.34/1.29
% 1.34/1.29 % ------ Proving...
% 1.34/1.29 %
% 1.34/1.29
% 1.34/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.29
% 1.34/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.34/1.29
% 1.34/1.29
%------------------------------------------------------------------------------