%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 2.19s 1.19s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 78 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)) = c_HOL_Oabs(c_times(X1,X2,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4,plain,
! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4] : ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f6,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f8,plain,
! [X2,X0,X1] : true = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X0,X1] : ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f10,plain,
! [X2,X0,X1] : true = ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0,X1] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f12,plain,
! [X0,X1] : true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f14,plain,
true = c_less(c_0,v_c,t_b),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f16,plain,
true = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f18,plain,
true = c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f20,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f21,plain,
true != c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f23,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f25,plain,
! [X0] : true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f27,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true),
inference(reorient_equations,[],[f26]) ).
fof(f28,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f29,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true),
inference(reorient_equations,[],[f28]) ).
fof(f30,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f31,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true),
inference(reorient_equations,[],[f30]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)) = c_HOL_Oabs(c_times(X1,X2,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true) = true,
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true) = true,
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true) = true,
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
inference(cnf_transformation,[],[f16]) ).
tcf(c_75,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
inference(cnf_transformation,[],[f18]) ).
tcf(c_76,negated_conjecture,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f19]) ).
tcf(c_77,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_78,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_79,plain,
! [X0: $i] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_80,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
inference(cnf_transformation,[],[f27]) ).
tcf(c_81,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
inference(cnf_transformation,[],[f29]) ).
tcf(c_82,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(cnf_transformation,[],[f31]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] : ifeq2(true,true,c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b)) = c_HOL_Oabs(c_times(X0,X1,t_b),t_b),
inference(superposition,[status(thm)],[c_78,c_68]) ).
tcf(c_282,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = true,
inference(superposition,[status(thm)],[c_78,c_80]) ).
tcf(c_283,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = true,
inference(superposition,[status(thm)],[c_78,c_81]) ).
tcf(c_284,plain,
ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = true,
inference(superposition,[status(thm)],[c_78,c_82]) ).
tcf(c_285,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(demodulation,[status(thm)],[c_282,c_67]) ).
tcf(c_288,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(demodulation,[status(thm)],[c_283,c_67]) ).
tcf(c_290,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(demodulation,[status(thm)],[c_284,c_67]) ).
tcf(c_292,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(superposition,[status(thm)],[c_290,c_79]) ).
tcf(c_293,plain,
class_Orderings_Oorder(t_b) = true,
inference(demodulation,[status(thm)],[c_292,c_67]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(c_times(X0,X1,t_b),t_b),
inference(demodulation,[status(thm)],[c_278,c_66]) ).
tcf(c_302,plain,
! [X0: $i] : ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),true) = true,
inference(superposition,[status(thm)],[c_290,c_72]) ).
tcf(c_304,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b) = true,
inference(demodulation,[status(thm)],[c_302,c_67]) ).
tcf(c_306,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = true,
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_311,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_0,v_c,t_b),true),true) = true,
inference(light_normalisation,[status(thm)],[c_306,c_293]) ).
tcf(c_317,plain,
c_lessequals(c_0,v_c,t_b) = true,
inference(demodulation,[status(thm)],[c_311,c_67]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] : ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(c_0,X1,t_b),true,c_lessequals(c_0,c_times(X0,X1,t_b),t_b),true),true),true) = true,
inference(superposition,[status(thm)],[c_285,c_70]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(X1,X0,t_b),true,ifeq(true,true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true) = true,
inference(superposition,[status(thm)],[c_75,c_69]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(X1,X0,t_b),true,ifeq(true,true,ifeq(true,true,c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true) = true,
inference(light_normalisation,[status(thm)],[c_358,c_288]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(X1,X0,t_b),true,c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
inference(demodulation,[status(thm)],[c_376,c_67,c_304]) ).
tcf(c_408,plain,
! [X0: $i] : ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,c_lessequals(c_times(X0,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
inference(superposition,[status(thm)],[c_76,c_400]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(c_0,X1,t_b),true,c_lessequals(c_0,c_times(X0,X1,t_b),t_b),true),true) = true,
inference(demodulation,[status(thm)],[c_329,c_67]) ).
tcf(c_458,plain,
! [X0: $i] : ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true),true) = true,
inference(superposition,[status(thm)],[c_317,c_456]) ).
tcf(c_476,plain,
! [X0: $i] : ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true) = true,
inference(demodulation,[status(thm)],[c_458,c_67]) ).
tcf(c_477,plain,
! [X0: $i] : ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b),true) = true,
inference(superposition,[status(thm)],[c_304,c_476]) ).
tcf(c_616,plain,
! [X0: $i] : c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b) = true,
inference(demodulation,[status(thm)],[c_477,c_67]) ).
tcf(c_620,plain,
! [X0: $i] : ifeq(true,true,ifeq(c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,c_lessequals(c_times(X0,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
inference(demodulation,[status(thm)],[c_408,c_616]) ).
tcf(c_827,plain,
! [X0: $i] : ifeq(c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,c_lessequals(c_times(X0,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true) = true,
inference(demodulation,[status(thm)],[c_620,c_67]) ).
tcf(c_828,plain,
ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),true) = true,
inference(superposition,[status(thm)],[c_74,c_827]) ).
tcf(c_846,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(demodulation,[status(thm)],[c_828,c_67,c_296]) ).
tcf(c_847,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_846,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:50:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.19/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.19/1.19 % SZS status Started for theBenchmark.p
% 2.19/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.19
% 2.19/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/1.19
% 2.19/1.19 % ------ iProver source info
% 2.19/1.19
% 2.19/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/1.19 % git: non_committed_changes: false
% 2.19/1.19
% 2.19/1.19 % ------ Parsing...% successful
% 2.19/1.19
% 2.19/1.19
% 2.19/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/1.19
% 2.19/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.19/1.19
% 2.19/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/1.19
% 2.19/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.19/1.19 % ------ Proving...
% 2.19/1.19 % ------ Problem Properties
% 2.19/1.19
% 2.19/1.19 %
% 2.19/1.19 % clauses 17
% 2.19/1.19 % conjectures 6
% 2.19/1.19 % EPR 0
% 2.19/1.19 % Horn 17
% 2.19/1.19 % unary 17
% 2.19/1.19 % binary 0
% 2.19/1.19 % lits 17
% 2.19/1.19 % lits eq 17
% 2.19/1.19 % fd_pure 0
% 2.19/1.19 % fd_pseudo 0
% 2.19/1.19 % fd_cond 0
% 2.19/1.19 % fd_pseudo_cond 0
% 2.19/1.19 % AC symbols 0
% 2.19/1.19
% 2.19/1.19 % ------ Input Options Time Limit: Unbounded
% 2.19/1.19
% 2.19/1.19
% 2.19/1.19 % ------
% 2.19/1.19 % Current options:
% 2.19/1.19 % ------
% 2.19/1.19
% 2.19/1.19
% 2.19/1.19 %
% 2.19/1.19
% 2.19/1.19 % ------ Proving...
% 2.19/1.19 %
% 2.19/1.19
% 2.19/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.19/1.19
% 2.19/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.19
% 2.19/1.19
%------------------------------------------------------------------------------