%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 12:55:09 PM UTC 2026
% Result : Unsatisfiable 14.46s 2.44s
% Output : Proof 14.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 85 unt; 0 def)
% Number of atoms : 181 ( 73 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 126 ( 66 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 160 ( 17 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f7_nnf,plain,
! [T_b,V_y,V_z,V_x] :
( c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T_b,V_y,V_z,V_x] :
( c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t20,plain,
ifeq(class_Orderings_Olinorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X3,X1),true,c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t32,plain,
ifeq(class_Orderings_Olinorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X3,X1),true,c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f3,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(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t36,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(f12,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(f12_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t7,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t28,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f2,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f2_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t0,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t39,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t41,plain,
true = ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true),
inference(cp,[status(thm)],[t28,t39]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t700,plain,
true = class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(step,[status(thm)],[t41,t21]) ).
cnf(t70,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(orient,[status(thm)],[t700]) ).
cnf(t71,plain,
true = ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),true),
inference(cp,[status(thm)],[t36,t70]) ).
cnf(t703,plain,
true = c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),
inference(step,[status(thm)],[t71,t21]) ).
cnf(t79,plain,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b) = true,
inference(orient,[status(thm)],[t703]) ).
cnf(t86,plain,
true = ifeq(class_Orderings_Olinorder(t_b),true,ifeq(true,true,ifeq(c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true,c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_HOL_Oabs(X2,t_b),t_b),true),true),true),
inference(cp,[status(thm)],[t32,t79]) ).
cnf(f11,axiom,
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f11_nnf,plain,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t9,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t27,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t42,plain,
true = ifeq(true,true,class_Orderings_Olinorder(t_b),true),
inference(cp,[status(thm)],[t27,t39]) ).
cnf(t701,plain,
true = class_Orderings_Olinorder(t_b),
inference(step,[status(thm)],[t42,t21]) ).
cnf(t72,plain,
class_Orderings_Olinorder(t_b) = true,
inference(orient,[status(thm)],[t701]) ).
cnf(t814,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true,c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_HOL_Oabs(X2,t_b),t_b),true),true),true),
inference(step,[status(thm)],[t86,t72]) ).
cnf(t815,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true,c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_HOL_Oabs(X2,t_b),t_b),true),true),
inference(step,[status(thm)],[t814,t21]) ).
cnf(t816,plain,
true = ifeq(c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true,c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_HOL_Oabs(X2,t_b),t_b),true),
inference(step,[status(thm)],[t815,t21]) ).
cnf(t669,plain,
ifeq(c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true,c_lessequals(c_Orderings_Omax(X1,c_0,t_b),c_HOL_Oabs(X2,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t816]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1_nnf,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t15,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t54,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(t681,plain,
true = ifeq(c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),true,false,true),
inference(cp,[status(thm)],[t669,t54]) ).
cnf(f8,axiom,
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f8_nnf,plain,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t19,plain,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X2,X1),true,c_lessequals(X4,X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t34,plain,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X2,X1),true,c_lessequals(X4,X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t81,plain,
true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(true,true,ifeq(c_lessequals(X1,c_0,t_b),true,c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true),true),true),
inference(cp,[status(thm)],[t34,t79]) ).
cnf(f10,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f10_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t6,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t31,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f13,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f13_nnf,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t8,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Opordered__ab__group__add(X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t26,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Opordered__ab__group__add(X1),true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t40,plain,
true = ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),
inference(cp,[status(thm)],[t26,t39]) ).
cnf(t699,plain,
true = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(step,[status(thm)],[t40,t21]) ).
cnf(t66,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(orient,[status(thm)],[t699]) ).
cnf(t67,plain,
true = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(cp,[status(thm)],[t31,t66]) ).
cnf(t702,plain,
true = class_Orderings_Oorder(t_b),
inference(step,[status(thm)],[t67,t21]) ).
cnf(t75,plain,
class_Orderings_Oorder(t_b) = true,
inference(orient,[status(thm)],[t702]) ).
cnf(t726,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(c_lessequals(X1,c_0,t_b),true,c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true),true),true),
inference(step,[status(thm)],[t81,t75]) ).
cnf(t727,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,c_0,t_b),true,c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true),true),
inference(step,[status(thm)],[t726,t21]) ).
cnf(t728,plain,
true = ifeq(c_lessequals(X1,c_0,t_b),true,c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true),
inference(step,[status(thm)],[t727,t21]) ).
cnf(t145,plain,
ifeq(c_lessequals(X1,c_0,t_b),true,c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t728]) ).
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,plain,
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t14,plain,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_less(X2,X3,X1),true,c_lessequals(X2,X3,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t35,plain,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_less(X2,X3,X1),true,c_lessequals(X2,X3,X1),true),true) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f6,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f6_nnf,plain,
! [T_a,V_y,V_x] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T_a,V_y,V_x] :
( c_lessequals(V_x,V_y,T_a)
| c_less(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t13,plain,
ifeq(class_Orderings_Olinorder(X1),true,or(c_less(X2,X3,X1),c_lessequals(X3,X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t33,plain,
ifeq(class_Orderings_Olinorder(X1),true,or(c_less(X2,X3,X1),c_lessequals(X3,X2,X1)),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t73,plain,
true = ifeq(true,true,or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)),true),
inference(cp,[status(thm)],[t33,t72]) ).
cnf(t704,plain,
true = or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)),
inference(step,[status(thm)],[t73,t21]) ).
cnf(t88,plain,
or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)) = true,
inference(orient,[status(thm)],[t704]) ).
cnf(f0,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f0_nnf,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t10,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t89,plain,
true = or(c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),false),
inference(cp,[status(thm)],[t88,t43]) ).
cnf(t1,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t22,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t708,plain,
true = c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(step,[status(thm)],[t89,t22]) ).
cnf(t100,plain,
c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) = true,
inference(orient,[status(thm)],[t708]) ).
cnf(t101,plain,
true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(true,true,c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),true),true),
inference(cp,[status(thm)],[t35,t100]) ).
cnf(t709,plain,
true = ifeq(true,true,ifeq(true,true,c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),true),true),
inference(step,[status(thm)],[t101,t75]) ).
cnf(t710,plain,
true = ifeq(true,true,c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),true),
inference(step,[status(thm)],[t709,t21]) ).
cnf(t711,plain,
true = c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(step,[status(thm)],[t710,t21]) ).
cnf(t102,plain,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) = true,
inference(orient,[status(thm)],[t711]) ).
cnf(t149,plain,
true = ifeq(true,true,c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b),true),
inference(cp,[status(thm)],[t145,t102]) ).
cnf(t730,plain,
true = c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(step,[status(thm)],[t149,t21]) ).
cnf(t163,plain,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b) = true,
inference(orient,[status(thm)],[t730]) ).
cnf(t817,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t681,t163]) ).
cnf(t818,plain,
true = false,
inference(step,[status(thm)],[t817,t21]) ).
cnf(t682,plain,
false = true,
inference(orient,[status(thm)],[t818]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t682]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 05:53:39 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.46/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.46/2.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------