%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA020-1 : 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 : n011.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 12:55:38 PM UTC 2026
% Result : Unsatisfiable 96.96s 15.97s
% Output : CNFRefutation 96.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 23 unt; 0 def)
% Number of atoms : 100 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 49 ~; 44 |; 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1418,axiom,
! [X0] :
( c_0 = c_HOL_Oabs(c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__0__eq_1) ).
fof(f1425,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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f1431,axiom,
! [X0,X1] :
( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f1432,plain,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = c_HOL_Oabs(c_uminus(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(reorient_equations,[],[f1431]) ).
fof(f3033,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f3037,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f3044,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f3364,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f3365,axiom,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f3368,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3369,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f3368]) ).
fof(f3370,negated_conjecture,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3372,negated_conjecture,
v_x = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3373,plain,
c_0 = v_x,
inference(reorient_equations,[],[f3372]) ).
fof(f3374,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3375,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3376,plain,
v_x = v_f(v_x),
inference(definition_unfolding,[],[f3369,f3373,f3373]) ).
fof(f3377,plain,
c_less(v_x,v_c,t_a),
inference(definition_unfolding,[],[f3370,f3373]) ).
fof(f3440,plain,
! [X0,X1] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f1425,f3373]) ).
fof(f3443,plain,
! [X0] :
( v_x = c_HOL_Oabs(v_x,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f1418,f3373,f3373]) ).
fof(f3694,plain,
! [X2,X0,X1] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ c_lessequals(v_x,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(definition_unfolding,[],[f3365,f3373,f3373,f3373]) ).
tcf(c_2840,negated_conjecture,
v_f(v_x) = v_x,
inference(cnf_transformation,[],[f3376]) ).
tcf(c_2841,negated_conjecture,
c_less(v_x,v_c,t_a),
inference(cnf_transformation,[],[f3377]) ).
tcf(c_2843,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[],[f3374]) ).
tcf(c_2844,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[],[f3375]) ).
tcf(c_2937,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f1432]) ).
tcf(c_2941,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f3440]) ).
tcf(c_2945,negated_conjecture,
! [X0: $i] :
( ( c_HOL_Oabs(v_x,X0) = v_x )
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f3443]) ).
tcf(c_3159,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3044]) ).
tcf(c_3606,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f3364]) ).
tcf(c_3610,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3037]) ).
tcf(c_3943,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,c_times(X2,X0,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(v_x,X2,X1)
| ~ c_lessequals(v_x,X0,X1) ),
inference(cnf_transformation,[],[f3694]) ).
tcf(c_3957,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3033]) ).
tcf(c_5422,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Oorder(X0) ),
inference(prop_impl_just,[status(thm)],[c_3610]) ).
tcf(c_5423,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_5422]) ).
tcf(c_6646,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(prop_impl_just,[status(thm)],[c_3159]) ).
tcf(c_6647,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_6646]) ).
tcf(c_7754,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(prop_impl_just,[status(thm)],[c_3957]) ).
tcf(c_21345,plain,
~ c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(light_normalisation,[status(thm)],[c_2843,c_2840]) ).
tcf(c_46611,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_2844,c_6647]) ).
tcf(c_46612,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(unflattening,[status(thm)],[c_46611]) ).
tcf(c_46621,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_2844,c_5423]) ).
tcf(c_46622,plain,
class_Orderings_Oorder(t_a),
inference(unflattening,[status(thm)],[c_46621]) ).
tcf(c_46626,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_2844,c_7754]) ).
tcf(c_46627,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(unflattening,[status(thm)],[c_46626]) ).
tcf(c_50317,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ c_lessequals(v_x,X1,X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_3943,c_46627]) ).
tcf(c_50318,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_times(X1,X0,t_a),t_a)
| ~ c_lessequals(v_x,X1,t_a)
| ~ c_lessequals(v_x,X0,t_a) ),
inference(unflattening,[status(thm)],[c_50317]) ).
tcf(c_101172,plain,
c_HOL_Oabs(v_x,t_a) = v_x,
inference(superposition,[status(thm)],[c_46612,c_2945]) ).
tcf(c_107202,plain,
~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(light_normalisation,[status(thm)],[c_21345,c_101172]) ).
tcf(c_114703,plain,
( c_lessequals(v_x,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(superposition,[status(thm)],[c_2841,c_3606]) ).
tcf(c_114766,plain,
c_lessequals(v_x,v_c,t_a),
inference(forward_subsumption_resolution,[status(thm)],[c_114703,c_46622]) ).
tcf(c_116623,plain,
! [X0: $i] : c_HOL_Oabs(c_uminus(X0,t_a),t_a) = c_HOL_Oabs(X0,t_a),
inference(superposition,[status(thm)],[c_46612,c_2937]) ).
tcf(c_193043,plain,
! [X0: $i] :
( c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(superposition,[status(thm)],[c_116623,c_2941]) ).
tcf(c_193044,plain,
! [X0: $i] : c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a),
inference(forward_subsumption_resolution,[status(thm)],[c_193043,c_46612]) ).
tcf(c_217613,plain,
( ~ c_lessequals(v_x,v_c,t_a)
| ~ c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(superposition,[status(thm)],[c_50318,c_107202]) ).
tcf(c_217614,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_217613,c_114766,c_193044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 05:46:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 96.96/15.97 % SZS status Started for theBenchmark.p
% 96.96/15.97 % SZS status Unsatisfiable for theBenchmark.p
% 96.96/15.97
% 96.96/15.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 96.96/15.97
% 96.96/15.97 % ------ iProver source info
% 96.96/15.97
% 96.96/15.97 % git: date: 2026-07-19 20:42:38 +0200
% 96.96/15.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 96.96/15.97 % git: non_committed_changes: false
% 96.96/15.97
% 96.96/15.97 % ------ Parsing...% successful
% 96.96/15.97
% 96.96/15.97
% 96.96/15.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 96.96/15.97
% 96.96/15.97 % ------ Preprocessing... sup_sim: 81 sf_s rm: 61 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 48 sf_s rm: 40 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe_e %
% 96.96/15.97
% 96.96/15.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 96.96/15.97
% 96.96/15.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 96.96/15.97 % ------ Proving...
% 96.96/15.97 % ------ Problem Properties
% 96.96/15.97
% 96.96/15.97 %
% 96.96/15.97 % clauses 972
% 96.96/15.97 % conjectures 172
% 96.96/15.97 % EPR 183
% 96.96/15.97 % Horn 866
% 96.96/15.97 % unary 275
% 96.96/15.97 % binary 485
% 96.96/15.97 % lits 1919
% 96.96/15.97 % lits eq 532
% 96.96/15.97 % fd_pure 0
% 96.96/15.97 % fd_pseudo 0
% 96.96/15.97 % fd_cond 57
% 96.96/15.97 % fd_pseudo_cond 38
% 96.96/15.97 % AC symbols 0
% 96.96/15.97
% 96.96/15.97 % ------ Schedule dynamic 5 is on
% 96.96/15.97
% 96.96/15.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 96.96/15.97
% 96.96/15.97
% 96.96/15.97 % ------
% 96.96/15.97 % Current options:
% 96.96/15.97 % ------
% 96.96/15.97
% 96.96/15.97
% 96.96/15.97 %
% 96.96/15.97
% 96.96/15.97 % ------ Proving...
% 96.96/15.97 %
% 96.96/15.97
% 96.96/15.97 % SZS status Unsatisfiable for theBenchmark.p
% 96.96/15.97
% 96.96/15.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 96.96/15.97
% 96.96/15.97
%------------------------------------------------------------------------------