%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA032-2 : 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 : n017.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 12:55:41 PM UTC 2026
% Result : Unsatisfiable 1.80s 1.28s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 67 ( 33 unt; 10 def)
% Number of atoms : 170 ( 38 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 56 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X2,X3,X0,X1] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_times(X1,X2,X0) = c_times(X2,X1,X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,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__left__mono_0) ).
fof(f5,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f7,axiom,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f8,axiom,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f9,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(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) ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_60,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,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X0,X2),c_times(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Opordered__semiring(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[],[f6]) ).
tcf(c_66,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f11]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_60]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_165]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_61]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_176]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(X2,X3,X1) = c_times(X3,X2,X1) )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_62]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_187]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_63]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X0,X2),c_times(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_198]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_188,c_70]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(unflattening,[status(thm)],[c_217]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_177,c_70]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(unflattening,[status(thm)],[c_223]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_166,c_70]) ).
tcf(c_230,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(unflattening,[status(thm)],[c_229]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_199]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_235]) ).
tcf(c_272,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_65,c_218]) ).
tcf(c_282,definition,
iPr_def_10 = v_b(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_283,definition,
iPr_def_11 = c_HOL_Oabs(iPr_def_10,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_284,definition,
iPr_def_12 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_285,definition,
iPr_def_13 = c_HOL_Oabs(iPr_def_12,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_286,definition,
iPr_def_14 = c_times(iPr_def_11,iPr_def_13,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_287,definition,
iPr_def_15 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_288,definition,
iPr_def_16 = c_HOL_Oabs(iPr_def_15,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_289,definition,
iPr_def_17 = c_times(iPr_def_16,iPr_def_13,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_290,definition,
iPr_def_18 = c_times(v_c,iPr_def_17,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_291,definition,
iPr_def_19 = c_times(v_c,iPr_def_16,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_292,plain,
~ c_lessequals(iPr_def_14,iPr_def_18,t_b),
inference(demodulation,[status(thm)],[c_272,c_287,c_288,c_289,c_290,c_284,c_285,c_282,c_283,c_286]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_236]) ).
tcf(c_294,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(demodulation,[status(thm)],[c_230]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(demodulation,[status(thm)],[c_224]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(demodulation,[status(thm)],[c_218]) ).
tcf(c_297,negated_conjecture,
c_lessequals(iPr_def_11,iPr_def_19,t_b),
inference(demodulation,[status(thm)],[c_64,c_291]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X0,X2,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_296,c_293]) ).
tcf(c_606,plain,
c_lessequals(c_0,iPr_def_13,t_b),
inference(superposition,[status(thm)],[c_285,c_294]) ).
tcf(c_925,plain,
! [X0: $i] :
( c_lessequals(iPr_def_14,c_times(iPr_def_13,X0,t_b),t_b)
| ~ c_lessequals(c_0,iPr_def_13,t_b)
| ~ c_lessequals(iPr_def_11,X0,t_b) ),
inference(superposition,[status(thm)],[c_286,c_488]) ).
tcf(c_927,plain,
! [X0: $i] :
( c_lessequals(iPr_def_14,c_times(iPr_def_13,X0,t_b),t_b)
| ~ c_lessequals(iPr_def_11,X0,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_925,c_606]) ).
tcf(c_1034,plain,
c_times(iPr_def_13,iPr_def_16,t_b) = iPr_def_17,
inference(demodulation,[status(thm)],[c_289,c_296]) ).
tcf(c_1042,plain,
! [X0: $i] : c_times(iPr_def_13,c_times(iPr_def_16,X0,t_b),t_b) = c_times(iPr_def_17,X0,t_b),
inference(superposition,[status(thm)],[c_1034,c_295]) ).
tcf(c_1122,plain,
c_times(iPr_def_17,v_c,t_b) = iPr_def_18,
inference(demodulation,[status(thm)],[c_290,c_296]) ).
tcf(c_1202,plain,
c_times(iPr_def_16,v_c,t_b) = iPr_def_19,
inference(demodulation,[status(thm)],[c_291,c_296]) ).
tcf(c_1493,plain,
c_times(iPr_def_13,iPr_def_19,t_b) = c_times(iPr_def_17,v_c,t_b),
inference(superposition,[status(thm)],[c_1202,c_1042]) ).
tcf(c_1514,plain,
c_times(iPr_def_13,iPr_def_19,t_b) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_1493,c_1122]) ).
tcf(c_3061,plain,
( c_lessequals(iPr_def_14,iPr_def_18,t_b)
| ~ c_lessequals(iPr_def_11,iPr_def_19,t_b) ),
inference(superposition,[status(thm)],[c_1514,c_927]) ).
tcf(c_3062,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3061,c_292,c_297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 05:44:16 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.80/1.28 % SZS status Started for theBenchmark.p
% 1.80/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.80/1.28
% 1.80/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.80/1.28
% 1.80/1.28 % ------ iProver source info
% 1.80/1.28
% 1.80/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.80/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.80/1.28 % git: non_committed_changes: false
% 1.80/1.28
% 1.80/1.28 % ------ Parsing...% successful
% 1.80/1.28
% 1.80/1.28
% 1.80/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.80/1.28
% 1.80/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.80/1.28
% 1.80/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.80/1.28
% 1.80/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.80/1.28 % ------ Proving...
% 1.80/1.28 % ------ Problem Properties
% 1.80/1.28
% 1.80/1.28 %
% 1.80/1.28 % clauses 16
% 1.80/1.28 % conjectures 1
% 1.80/1.28 % EPR 2
% 1.80/1.28 % Horn 16
% 1.80/1.28 % unary 15
% 1.80/1.28 % binary 0
% 1.80/1.28 % lits 18
% 1.80/1.28 % lits eq 12
% 1.80/1.28 % fd_pure 0
% 1.80/1.28 % fd_pseudo 0
% 1.80/1.28 % fd_cond 0
% 1.80/1.28 % fd_pseudo_cond 0
% 1.80/1.28 % AC symbols 0
% 1.80/1.28
% 1.80/1.28 % ------ Schedule dynamic 5 is on
% 1.80/1.28
% 1.80/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.80/1.28
% 1.80/1.28
% 1.80/1.28 % ------
% 1.80/1.28 % Current options:
% 1.80/1.28 % ------
% 1.80/1.28
% 1.80/1.28
% 1.80/1.28 %
% 1.80/1.28
% 1.80/1.28 % ------ Proving...
% 1.80/1.28 %
% 1.80/1.28
% 1.80/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.80/1.28
% 1.80/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.80/1.28
% 1.80/1.28
%------------------------------------------------------------------------------