%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 12:55:42 PM UTC 2026
% Result : Unsatisfiable 2.86s 1.49s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 48 ( 26 unt; 6 def)
% Number of atoms : 110 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 40 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
fof(f5,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
fof(f8,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f9,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f10,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tcf(c_59,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X0,X3,X2),c_times(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__semiring(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_118,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_61,c_68]) ).
tcf(c_122,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[c_61,c_67]) ).
tcf(c_126,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolution,[status(thm)],[c_61,c_66]) ).
tcf(c_133,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[c_63,c_118]) ).
tcf(c_138,plain,
! [X0: $i] : c_lessequals(X0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[c_62,c_118]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_a)
| ~ c_lessequals(X2,X0,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(resolution,[status(thm)],[c_64,c_122]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X0,X2,t_a),c_times(X1,X2,t_a),t_a)
| ~ c_lessequals(c_0,X2,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(resolution,[status(thm)],[c_65,c_126]) ).
tcf(c_192,definition,
iPr_def_10 = v_h(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_193,definition,
iPr_def_11 = c_HOL_Oabs(iPr_def_10,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_194,definition,
iPr_def_12 = c_HOL_Oabs(v_c,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_195,definition,
iPr_def_13 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_196,definition,
iPr_def_14 = c_HOL_Oabs(iPr_def_13,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_197,definition,
iPr_def_15 = c_times(iPr_def_12,iPr_def_14,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X0,X2,t_a),c_times(X1,X2,t_a),t_a)
| ~ c_lessequals(c_0,X2,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_a)
| ~ c_lessequals(X2,X0,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(demodulation,[status(thm)],[c_145]) ).
tcf(c_200,plain,
! [X0: $i] : c_lessequals(X0,c_HOL_Oabs(X0,t_a),t_a),
inference(demodulation,[status(thm)],[c_138]) ).
tcf(c_201,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_202,negated_conjecture,
~ c_lessequals(iPr_def_11,iPr_def_15,t_a),
inference(demodulation,[status(thm)],[c_60,c_195,c_196,c_194,c_197,c_192,c_193]) ).
tcf(c_203,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_times(X3,X2,t_a),t_a)
| ~ c_lessequals(c_0,X2,t_a)
| ~ c_lessequals(X1,X3,t_a)
| ~ c_lessequals(X0,c_times(X1,X2,t_a),t_a) ),
inference(superposition,[status(thm)],[c_198,c_199]) ).
tcf(c_418,plain,
c_lessequals(c_HOL_Oabs(iPr_def_10,t_a),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(superposition,[status(thm)],[c_192,c_203]) ).
tcf(c_420,plain,
c_lessequals(iPr_def_11,c_times(v_c,iPr_def_14,t_a),t_a),
inference(light_normalisation,[status(thm)],[c_418,c_193,c_195,c_196]) ).
tcf(c_441,plain,
c_lessequals(v_c,iPr_def_12,t_a),
inference(superposition,[status(thm)],[c_194,c_200]) ).
tcf(c_521,plain,
c_lessequals(c_0,iPr_def_14,t_a),
inference(superposition,[status(thm)],[c_196,c_201]) ).
tcf(c_1592,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,c_times(X0,iPr_def_14,t_a),t_a)
| ~ c_lessequals(c_0,iPr_def_14,t_a)
| ~ c_lessequals(v_c,X0,t_a) ),
inference(superposition,[status(thm)],[c_420,c_413]) ).
tcf(c_1599,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,c_times(X0,iPr_def_14,t_a),t_a)
| ~ c_lessequals(v_c,X0,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1592,c_521]) ).
tcf(c_3697,plain,
( c_lessequals(iPr_def_11,iPr_def_15,t_a)
| ~ c_lessequals(v_c,iPr_def_12,t_a) ),
inference(superposition,[status(thm)],[c_197,c_1599]) ).
tcf(c_3707,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3697,c_202,c_441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 % Computer : n015.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 05:53:27 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.48 Running first-order theorem proving
% 0.14/0.48 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
% 0.14/0.50
% 0.14/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.50
% 0.14/0.50 % Detected problem language: tptp
% 0.22/0.52 % Proving...
% 2.86/1.49 % SZS status Started for theBenchmark.p
% 2.86/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 2.86/1.49
% 2.86/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.86/1.49
% 2.86/1.49 % ------ iProver source info
% 2.86/1.49
% 2.86/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.86/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.86/1.49 % git: non_committed_changes: false
% 2.86/1.49
% 2.86/1.49 % ------ Parsing...% successful
% 2.86/1.49
% 2.86/1.49
% 2.86/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.86/1.49
% 2.86/1.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.86/1.49
% 2.86/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.86/1.49
% 2.86/1.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.86/1.49 % ------ Proving...
% 2.86/1.49 % ------ Problem Properties
% 2.86/1.49
% 2.86/1.49 %
% 2.86/1.49 % clauses 12
% 2.86/1.49 % conjectures 2
% 2.86/1.49 % EPR 2
% 2.86/1.49 % Horn 12
% 2.86/1.49 % unary 10
% 2.86/1.49 % binary 0
% 2.86/1.49 % lits 16
% 2.86/1.49 % lits eq 6
% 2.86/1.49 % fd_pure 0
% 2.86/1.49 % fd_pseudo 0
% 2.86/1.49 % fd_cond 0
% 2.86/1.49 % fd_pseudo_cond 0
% 2.86/1.49 % AC symbols 0
% 2.86/1.49
% 2.86/1.49 % ------ Schedule dynamic 5 is on
% 2.86/1.49
% 2.86/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.86/1.49
% 2.86/1.49
% 2.86/1.49 % ------
% 2.86/1.49 % Current options:
% 2.86/1.49 % ------
% 2.86/1.49
% 2.86/1.49
% 2.86/1.49 %
% 2.86/1.49
% 2.86/1.49 % ------ Proving...
% 2.86/1.49 %
% 2.86/1.49
% 2.86/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 2.86/1.49
% 2.86/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.86/1.49
% 2.86/1.49
%------------------------------------------------------------------------------