%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA009-2 : 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 : 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 12:55:36 PM UTC 2026
% Result : Unsatisfiable 1.63s 1.26s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 18 unt; 4 def)
% Number of atoms : 74 ( 15 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_plus(X1,X3,X0),c_plus(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f2,axiom,
! [X0,X1] :
( c_plus(X1,c_uminus(X1,X0),X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f3,negated_conjecture,
! [X0] : c_lessequals(v_lb(X0),v_f(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f6,axiom,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_plus(X0,X3,X2),c_plus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( c_plus(X1,c_uminus(X1,X0),X0) = c_0 )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] : c_lessequals(v_lb(X0),v_f(X0),t_b),
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_62,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f7]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(X2,c_uminus(X2,X1),X1) = c_0 )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_57]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( c_plus(X1,c_uminus(X1,X0),X0) = c_0 )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_117]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( ( c_plus(X1,c_uminus(X1,X0),X0) = c_0 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_118,c_62]) ).
tcf(c_129,plain,
! [X0: $i] : c_plus(X0,c_uminus(X0,t_b),t_b) = c_0,
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_134,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_62]) ).
tcf(c_135,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(unflattening,[status(thm)],[c_134]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_plus(X1,X3,X0),c_plus(X2,X3,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_135]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_plus(X0,X2,t_b),c_plus(X1,X2,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_141]) ).
tcf(c_172,definition,
iPr_def_10 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_173,definition,
iPr_def_11 = v_lb(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_174,definition,
iPr_def_12 = c_uminus(iPr_def_11,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_175,definition,
iPr_def_13 = c_plus(iPr_def_10,iPr_def_12,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_plus(X0,X2,t_b),c_plus(X1,X2,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_142]) ).
tcf(c_177,plain,
! [X0: $i] : c_plus(X0,c_uminus(X0,t_b),t_b) = c_0,
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_178,negated_conjecture,
~ c_lessequals(c_0,iPr_def_13,t_b),
inference(demodulation,[status(thm)],[c_59,c_173,c_174,c_172,c_175]) ).
tcf(c_179,negated_conjecture,
! [X0: $i] : c_lessequals(v_lb(X0),v_f(X0),t_b),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_plus(X1,c_uminus(X0,t_b),t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_177,c_176]) ).
tcf(c_340,plain,
c_lessequals(v_lb(v_x),iPr_def_10,t_b),
inference(superposition,[status(thm)],[c_172,c_179]) ).
tcf(c_341,plain,
c_lessequals(iPr_def_11,iPr_def_10,t_b),
inference(light_normalisation,[status(thm)],[c_340,c_173]) ).
tcf(c_345,plain,
! [X0: $i] :
( c_lessequals(c_0,c_plus(X0,iPr_def_12,t_b),t_b)
| ~ c_lessequals(iPr_def_11,X0,t_b) ),
inference(superposition,[status(thm)],[c_174,c_314]) ).
tcf(c_381,plain,
( c_lessequals(c_0,iPr_def_13,t_b)
| ~ c_lessequals(iPr_def_11,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_175,c_345]) ).
tcf(c_383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_381,c_178,c_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 05:46:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.63/1.26 % SZS status Started for theBenchmark.p
% 1.63/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.26
% 1.63/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.63/1.26
% 1.63/1.26 % ------ iProver source info
% 1.63/1.26
% 1.63/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.63/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.63/1.26 % git: non_committed_changes: false
% 1.63/1.26
% 1.63/1.26 % ------ Parsing...% successful
% 1.63/1.26
% 1.63/1.26
% 1.63/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.63/1.26
% 1.63/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.63/1.26
% 1.63/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.63/1.26
% 1.63/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.63/1.26 % ------ Proving...
% 1.63/1.26 % ------ Problem Properties
% 1.63/1.26
% 1.63/1.26 %
% 1.63/1.26 % clauses 8
% 1.63/1.26 % conjectures 2
% 1.63/1.26 % EPR 1
% 1.63/1.26 % Horn 8
% 1.63/1.26 % unary 7
% 1.63/1.26 % binary 1
% 1.63/1.26 % lits 9
% 1.63/1.26 % lits eq 5
% 1.63/1.26 % fd_pure 0
% 1.63/1.26 % fd_pseudo 0
% 1.63/1.26 % fd_cond 0
% 1.63/1.26 % fd_pseudo_cond 0
% 1.63/1.26 % AC symbols 0
% 1.63/1.26
% 1.63/1.26 % ------ Schedule dynamic 5 is on
% 1.63/1.26
% 1.63/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.63/1.26
% 1.63/1.26
% 1.63/1.26 % ------
% 1.63/1.26 % Current options:
% 1.63/1.26 % ------
% 1.63/1.26
% 1.63/1.26
% 1.63/1.26 %
% 1.63/1.26
% 1.63/1.26 % ------ Proving...
% 1.63/1.26 %
% 1.63/1.26
% 1.63/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 1.63/1.26
% 1.63/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.63/1.26
% 1.63/1.26
%------------------------------------------------------------------------------