%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA018-2 : 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 : n004.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 12:55:37 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.08s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 30 unt; 6 def)
% Number of atoms : 154 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 128 ( 66 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 15 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 92 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f6,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(f7,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(f8,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(f9,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(f10,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f11,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(f12,axiom,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f13,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) ).
tcf(c_62,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,negated_conjecture,
c_less(c_0,v_ca,t_b),
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,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,[],[f6]) ).
tcf(c_68,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,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,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,[],[f9]) ).
tcf(c_71,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,plain,
( class_LOrder_Ojoin__semilorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_78,plain,
( class_Orderings_Oorder(t_b)
| ~ class_LOrder_Ojoin__semilorder(t_b) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| ( X2 != v_ca )
| ( X1 != c_0 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_69]) ).
tcf(c_187,plain,
( c_lessequals(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(unflattening,[status(thm)],[c_186]) ).
tcf(c_188,plain,
c_lessequals(c_0,v_ca,t_b),
inference(global_subsumption_just,[status(thm)],[c_187,c_66,c_76,c_78,c_187]) ).
tcf(c_194,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_72,c_67]) ).
tcf(c_195,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_194]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_71]) ).
tcf(c_206,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_205]) ).
tcf(c_216,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_206]) ).
tcf(c_217,plain,
class_Orderings_Oorder(t_b),
inference(unflattening,[status(thm)],[c_216]) ).
tcf(c_221,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_66,c_195]) ).
tcf(c_222,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_221]) ).
tcf(c_227,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_74]) ).
tcf(c_228,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(unflattening,[status(thm)],[c_227]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_217]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_235]) ).
tcf(c_249,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_228]) ).
tcf(c_250,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_249]) ).
tcf(c_289,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_65,c_222]) ).
tcf(c_304,definition,
iPr_def_10 = v_x(v_xa),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_305,definition,
iPr_def_11 = c_HOL_Oabs(iPr_def_10,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_306,definition,
iPr_def_12 = v_g(v_xa),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_307,definition,
iPr_def_13 = c_HOL_Oabs(iPr_def_12,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_308,definition,
iPr_def_14 = c_times(v_c,iPr_def_13,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_309,definition,
iPr_def_15 = c_times(v_ca,iPr_def_14,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_310,plain,
~ c_lessequals(iPr_def_11,iPr_def_15,t_b),
inference(demodulation,[status(thm)],[c_289,c_306,c_307,c_308,c_309,c_304,c_305]) ).
tcf(c_311,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_250]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_236]) ).
tcf(c_314,plain,
c_lessequals(c_0,v_ca,t_b),
inference(demodulation,[status(thm)],[c_188]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_x(X0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X0),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_316,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_f(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_537,plain,
c_lessequals(c_HOL_Oabs(iPr_def_10,t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),t_b),
inference(superposition,[status(thm)],[c_304,c_315]) ).
tcf(c_538,plain,
c_lessequals(iPr_def_11,c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),t_b),
inference(light_normalisation,[status(thm)],[c_537,c_305]) ).
tcf(c_539,plain,
c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),c_times(v_c,c_HOL_Oabs(iPr_def_12,t_b),t_b),t_b),
inference(superposition,[status(thm)],[c_306,c_316]) ).
tcf(c_541,plain,
c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),iPr_def_14,t_b),
inference(light_normalisation,[status(thm)],[c_539,c_307,c_308]) ).
tcf(c_560,plain,
! [X0: $i] :
( c_lessequals(c_times(v_ca,X0,t_b),iPr_def_15,t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| ~ c_lessequals(X0,iPr_def_14,t_b) ),
inference(superposition,[status(thm)],[c_309,c_311]) ).
tcf(c_561,plain,
! [X0: $i] :
( c_lessequals(c_times(v_ca,X0,t_b),iPr_def_15,t_b)
| ~ c_lessequals(X0,iPr_def_14,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_560,c_314]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,iPr_def_15,t_b)
| ~ c_lessequals(X1,iPr_def_14,t_b)
| ~ c_lessequals(X0,c_times(v_ca,X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_561,c_312]) ).
tcf(c_753,plain,
( c_lessequals(iPr_def_11,iPr_def_15,t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),iPr_def_14,t_b) ),
inference(superposition,[status(thm)],[c_538,c_605]) ).
tcf(c_758,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_753,c_310,c_541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 05:45:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.65/1.08 % SZS status Started for theBenchmark.p
% 1.65/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 1.65/1.08
% 1.65/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.08
% 1.65/1.08 % ------ iProver source info
% 1.65/1.08
% 1.65/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.08 % git: non_committed_changes: false
% 1.65/1.08
% 1.65/1.08 % ------ Parsing...% successful
% 1.65/1.08
% 1.65/1.08
% 1.65/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.08
% 1.65/1.08 % ------ 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: 3 0s sf_e pe_s pe_e %
% 1.65/1.08
% 1.65/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.08
% 1.65/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.08 % ------ Proving...
% 1.65/1.08 % ------ Problem Properties
% 1.65/1.08
% 1.65/1.08 %
% 1.65/1.08 % clauses 13
% 1.65/1.08 % conjectures 2
% 1.65/1.08 % EPR 3
% 1.65/1.08 % Horn 13
% 1.65/1.08 % unary 11
% 1.65/1.08 % binary 0
% 1.65/1.08 % lits 17
% 1.65/1.08 % lits eq 7
% 1.65/1.08 % fd_pure 0
% 1.65/1.08 % fd_pseudo 0
% 1.65/1.08 % fd_cond 0
% 1.65/1.08 % fd_pseudo_cond 0
% 1.65/1.08 % AC symbols 0
% 1.65/1.08
% 1.65/1.08 % ------ Schedule dynamic 5 is on
% 1.65/1.08
% 1.65/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.65/1.08
% 1.65/1.08
% 1.65/1.08 % ------
% 1.65/1.08 % Current options:
% 1.65/1.08 % ------
% 1.65/1.08
% 1.65/1.08
% 1.65/1.08 %
% 1.65/1.08
% 1.65/1.08 % ------ Proving...
% 1.65/1.08 %
% 1.65/1.08
% 1.65/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 1.65/1.08
% 1.65/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.08
% 1.65/1.08
%------------------------------------------------------------------------------