%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 12:55:10 PM UTC 2026
% Result : Unsatisfiable 24.67s 3.91s
% Output : Proof 24.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 50 unt; 0 def)
% Number of atoms : 150 ( 37 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 134 ( 70 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 106 ( 5 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f14_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi13,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f10,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f10_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi9,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h0,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi9]) ).
cnf(f11,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f11_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h4,plain,
class_Orderings_Oorder(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi10,h0]) ).
cnf(f3,axiom,
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f3_nnf,plain,
! [T_a,V_x,V_y] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_x,V_y] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(class_Orderings_Oorder(X0),true,ifeq(c_less(X1,X2,X0),true,c_lessequals(X1,X2,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5_nnf,plain,
c_less(c_0,v_c,t_b),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
c_less(c_0,v_c,t_b),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h6,plain,
c_lessequals(c_0,v_c,t_b) = true,
inference(hyper_resolution,[status(thm)],[hi3,h4,hi5]) ).
cnf(f4,axiom,
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f4_nnf,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h5,plain,
c_lessequals(c_0,c_HOL_Oabs(V0,t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0]) ).
cnf(f12,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f12_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi11,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h2,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi9]) ).
cnf(f2,axiom,
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f2_nnf,plain,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( 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) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
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(X2,X1,X0),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h11,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(V0,t_b),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h5,h6]) ).
cnf(f13,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f13_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi12,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h1,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi9]) ).
cnf(f1,axiom,
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f1_nnf,plain,
! [T_a,V_c,V_d,V_a,V_b] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [T_a,V_c,V_d,V_a,V_b] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(c_times(X3,X1,X0),c_times(X4,X2,X0),X0)
| ~ c_lessequals(c_0,X4,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(class_Ring__and__Field_Opordered__semiring(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X3,X4,X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X4,X0),true,c_lessequals(c_times(X3,X1,X0),c_times(X4,X2,X0),X0),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f7,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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f7_nnf,plain,
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(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
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(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,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(equality_encoding,[status(esa)],[c7]) ).
cnf(f6,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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6_nnf,plain,
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(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
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(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,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(equality_encoding,[status(esa)],[c6]) ).
cnf(t35,plain,
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,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),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1,hi7,hi6,h5,h11]) ).
cnf(f0,axiom,
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f0_nnf,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,c_HOL_Oabs(c_times(X1,X2,X0),X0),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t14,plain,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(hyper_resolution,[status(thm)],[hi0,hi9]) ).
cnf(t260,plain,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(orient,[status(thm)],[t14]) ).
cnf(t323,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,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),t_b) = true,
inference(step,[status(thm)],[t35,t260]) ).
cnf(f8,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(f8_nnf,plain,
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),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
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),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t36,plain,
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(equality_encoding,[status(esa)],[c8]) ).
cnf(t257,plain,
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(orient,[status(thm)],[t36]) ).
cnf(t324,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(step,[status(thm)],[t323,t257]) ).
cnf(t291,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(orient,[status(thm)],[t324]) ).
cnf(f9,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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f9_nnf,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),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,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),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,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),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,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(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t291]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 05:52:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.67/3.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.67/3.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------