%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 5.94s 1.28s
% Output : Proof 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 14
% Syntax : Number of formulae : 154 ( 114 unt; 0 def)
% Number of atoms : 202 ( 122 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 331 ( 2 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
fof(f4_nnf,plain,
! [T_a,V_a,V_c,V_b] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a,V_c,V_b] :
( c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(c_minus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_plus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t16,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(X2,c_plus(X3,X4,X1),X1),true,c_lessequals(c_minus(X2,X4,X1),X3,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t28,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(X2,c_plus(X3,X4,X1),X1),true,c_lessequals(c_minus(X2,X4,X1),X3,X1),true),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f2,axiom,
( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
fof(f2_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_plus(c_minus(V_a,V_b,T_a),V_c,T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_plus(c_minus(X1,X2,X0),X3,X0) = c_minus(c_plus(X1,X3,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t20,plain,
ifeq(class_OrderedGroup_Oab__group__add(X1),true,c_plus(c_minus(X2,X3,X1),X4,X1),c_minus(c_plus(X2,X4,X1),X3,X1)) = c_minus(c_plus(X2,X4,X1),X3,X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t59,plain,
ifeq(class_OrderedGroup_Oab__group__add(X1),true,c_plus(c_minus(X2,X3,X1),X4,X1),c_minus(c_plus(X2,X4,X1),X3,X1)) = c_minus(c_plus(X2,X4,X1),X3,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(f10,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f10_nnf,plain,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi9,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Oab__group__add(X0),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f12,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f12_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h1,plain,
class_OrderedGroup_Oab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi11]) ).
cnf(f6,axiom,
( c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f6_nnf,plain,
! [T_a,V_a] :
( c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T_a,V_a] :
( c_minus(V_a,V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_minus(X1,X1,X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(class_OrderedGroup_Oab__group__add(X0),true,c_minus(X1,X1,X0),c_0) = c_0,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t4,plain,
c_minus(X1,X1,t_b) = c_0,
inference(hyper_resolution,[status(thm)],[hi6,h1]) ).
cnf(t42,plain,
c_minus(X1,X1,t_b) = c_0,
inference(orient,[status(thm)],[t4]) ).
cnf(t61,plain,
c_minus(c_plus(X1,X2,t_b),X1,t_b) = ifeq(class_OrderedGroup_Oab__group__add(t_b),true,c_plus(c_0,X2,t_b),c_minus(c_plus(X1,X2,t_b),X1,t_b)),
inference(cp,[status(thm)],[t59,t42]) ).
cnf(f3,axiom,
( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
fof(f3_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_minus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_c,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_minus(X1,c_minus(X2,X3,X0),X0) = c_minus(c_plus(X1,X3,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(class_OrderedGroup_Oab__group__add(X0),true,c_minus(X1,c_minus(X2,X3,X0),X0),c_minus(c_plus(X1,X3,X0),X2,X0)) = c_minus(c_plus(X1,X3,X0),X2,X0),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t13,plain,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_minus(X1,c_minus(X3,X2,t_b),t_b),
inference(hyper_resolution,[status(thm)],[hi3,h1]) ).
cnf(t45,plain,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_minus(X1,c_minus(X3,X2,t_b),t_b),
inference(orient,[status(thm)],[t13]) ).
cnf(f1,axiom,
( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
fof(f1_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_plus(V_a,c_minus(V_b,V_c,T_a),T_a) = c_minus(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_plus(X1,c_minus(X2,X3,X0),X0) = c_minus(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(class_OrderedGroup_Oab__group__add(X0),true,c_plus(X1,c_minus(X2,X3,X0),X0),c_minus(c_plus(X1,X2,X0),X3,X0)) = c_minus(c_plus(X1,X2,X0),X3,X0),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t14,plain,
c_plus(X1,c_minus(X2,X3,t_b),t_b) = c_minus(c_plus(X1,X2,t_b),X3,t_b),
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
cnf(t1451,plain,
c_plus(X1,c_minus(X2,X3,t_b),t_b) = c_minus(X1,c_minus(X3,X2,t_b),t_b),
inference(step,[status(thm)],[t14,t45]) ).
cnf(t66,plain,
c_minus(X1,c_minus(X2,X3,t_b),t_b) = c_plus(X1,c_minus(X3,X2,t_b),t_b),
inference(orient,[status(thm)],[t1451]) ).
cnf(t1452,plain,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X2,X3,t_b),t_b),
inference(step,[status(thm)],[t45,t66]) ).
cnf(t67,plain,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X2,X3,t_b),t_b),
inference(orient,[status(thm)],[t1452]) ).
cnf(t1462,plain,
c_plus(X1,c_minus(X2,X1,t_b),t_b) = ifeq(class_OrderedGroup_Oab__group__add(t_b),true,c_plus(c_0,X2,t_b),c_minus(c_plus(X1,X2,t_b),X1,t_b)),
inference(step,[status(thm)],[t61,t67]) ).
cnf(t0,plain,
class_OrderedGroup_Oab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi11]) ).
cnf(t32,plain,
class_OrderedGroup_Oab__group__add(t_b) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t1463,plain,
c_plus(X1,c_minus(X2,X1,t_b),t_b) = ifeq(true,true,c_plus(c_0,X2,t_b),c_minus(c_plus(X1,X2,t_b),X1,t_b)),
inference(step,[status(thm)],[t1462,t32]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t1464,plain,
c_plus(X1,c_minus(X2,X1,t_b),t_b) = c_plus(c_0,X2,t_b),
inference(step,[status(thm)],[t1463,t22]) ).
cnf(f9,axiom,
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f9_nnf,plain,
! [T] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_OrderedGroup_Ocomm__monoid__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h2,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi11]) ).
cnf(f0,axiom,
( c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f0_nnf,plain,
! [T_a,V_y] :
( c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [T_a,V_y] :
( c_plus(c_0,V_y,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
c_plus(c_0,X1,t_b) = X1,
inference(hyper_resolution,[status(thm)],[hi0,h2]) ).
cnf(t21,plain,
c_plus(c_0,X1,t_b) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t1465,plain,
c_plus(X1,c_minus(X2,X1,t_b),t_b) = X2,
inference(step,[status(thm)],[t1464,t21]) ).
cnf(t104,plain,
c_plus(X1,c_minus(X2,X1,t_b),t_b) = X2,
inference(orient,[status(thm)],[t1465]) ).
cnf(t110,plain,
c_plus(X1,X2,t_b) = c_plus(X3,c_plus(X1,c_minus(X2,X3,t_b),t_b),t_b),
inference(cp,[status(thm)],[t104,t67]) ).
cnf(t145,plain,
c_plus(X1,c_plus(X2,c_minus(X3,X1,t_b),t_b),t_b) = c_plus(X2,X3,t_b),
inference(orient,[status(thm)],[t110]) ).
cnf(t148,plain,
c_plus(X1,X2,t_b) = c_plus(X2,c_plus(X1,c_0,t_b),t_b),
inference(cp,[status(thm)],[t145,t42]) ).
cnf(t105,plain,
X1 = c_minus(X1,c_0,t_b),
inference(cp,[status(thm)],[t104,t21]) ).
cnf(t19,plain,
ifeq(class_OrderedGroup_Oab__group__add(X1),true,c_plus(X2,c_minus(X3,X4,X1),X1),c_minus(c_plus(X2,X3,X1),X4,X1)) = c_minus(c_plus(X2,X3,X1),X4,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t51,plain,
ifeq(class_OrderedGroup_Oab__group__add(X1),true,c_plus(X2,c_minus(X3,X4,X1),X1),c_minus(c_plus(X2,X3,X1),X4,X1)) = c_minus(c_plus(X2,X3,X1),X4,X1),
inference(orient,[status(thm)],[t19]) ).
cnf(t54,plain,
c_minus(c_plus(X1,X2,t_b),X2,t_b) = ifeq(class_OrderedGroup_Oab__group__add(t_b),true,c_plus(X1,c_0,t_b),c_minus(c_plus(X1,X2,t_b),X2,t_b)),
inference(cp,[status(thm)],[t51,t42]) ).
cnf(t1455,plain,
c_minus(X1,c_minus(X2,X2,t_b),t_b) = ifeq(class_OrderedGroup_Oab__group__add(t_b),true,c_plus(X1,c_0,t_b),c_minus(c_plus(X1,X2,t_b),X2,t_b)),
inference(step,[status(thm)],[t54,t45]) ).
cnf(t1456,plain,
c_minus(X1,c_0,t_b) = ifeq(class_OrderedGroup_Oab__group__add(t_b),true,c_plus(X1,c_0,t_b),c_minus(c_plus(X1,X2,t_b),X2,t_b)),
inference(step,[status(thm)],[t1455,t42]) ).
cnf(t1457,plain,
c_minus(X1,c_0,t_b) = ifeq(true,true,c_plus(X1,c_0,t_b),c_minus(c_plus(X1,X2,t_b),X2,t_b)),
inference(step,[status(thm)],[t1456,t32]) ).
cnf(t1458,plain,
c_minus(X1,c_0,t_b) = c_plus(X1,c_0,t_b),
inference(step,[status(thm)],[t1457,t22]) ).
cnf(t89,plain,
c_minus(X1,c_0,t_b) = c_plus(X1,c_0,t_b),
inference(orient,[status(thm)],[t1458]) ).
cnf(t1466,plain,
X1 = c_plus(X1,c_0,t_b),
inference(step,[status(thm)],[t105,t89]) ).
cnf(t116,plain,
c_plus(X1,c_0,t_b) = X1,
inference(orient,[status(thm)],[t1466]) ).
cnf(t1475,plain,
c_plus(X1,X2,t_b) = c_plus(X2,X1,t_b),
inference(step,[status(thm)],[t148,t116]) ).
cnf(t156,plain,
c_plus(X1,X2,t_b) = c_plus(X2,X1,t_b),
inference(orient,[status(thm)],[t1475]) ).
cnf(t163,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X1,c_plus(X2,X3,t_b),t_b),true,c_lessequals(c_minus(X1,X2,t_b),X3,t_b),true),true),
inference(cp,[status(thm)],[t28,t156]) ).
cnf(f11,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(f11_nnf,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi10,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t2,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi11]) ).
cnf(t38,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t1539,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,c_plus(X2,X3,t_b),t_b),true,c_lessequals(c_minus(X1,X2,t_b),X3,t_b),true),true),
inference(step,[status(thm)],[t163,t38]) ).
cnf(t1540,plain,
true = ifeq(c_lessequals(X1,c_plus(X2,X3,t_b),t_b),true,c_lessequals(c_minus(X1,X2,t_b),X3,t_b),true),
inference(step,[status(thm)],[t1539,t22]) ).
cnf(t1415,plain,
ifeq(c_lessequals(X1,c_plus(X2,X3,t_b),t_b),true,c_lessequals(c_minus(X1,X2,t_b),X3,t_b),true) = true,
inference(orient,[status(thm)],[t1540]) ).
cnf(f5,axiom,
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f5_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t17,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t30,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t40,plain,
true = ifeq(true,true,ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),true),
inference(cp,[status(thm)],[t30,t38]) ).
cnf(t1518,plain,
true = ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),
inference(step,[status(thm)],[t40,t22]) ).
cnf(t1134,plain,
ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t1518]) ).
cnf(t114,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_minus(X1,c_minus(X2,X3,t_b),t_b),X3,t_b),true),true),
inference(cp,[status(thm)],[t28,t104]) ).
cnf(t1519,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_minus(X1,c_minus(X2,X3,t_b),t_b),X3,t_b),true),true),
inference(step,[status(thm)],[t114,t38]) ).
cnf(t1520,plain,
true = ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_minus(X1,c_minus(X2,X3,t_b),t_b),X3,t_b),true),
inference(step,[status(thm)],[t1519,t22]) ).
cnf(t1521,plain,
true = ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_plus(X1,c_minus(X3,X2,t_b),t_b),X3,t_b),true),
inference(step,[status(thm)],[t1520,t66]) ).
cnf(t1165,plain,
ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_plus(X1,c_minus(X3,X2,t_b),t_b),X3,t_b),true) = true,
inference(orient,[status(thm)],[t1521]) ).
cnf(t43,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X1,c_plus(X2,X1,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true),true),
inference(cp,[status(thm)],[t28,t42]) ).
cnf(t1495,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,c_plus(X2,X1,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true),true),
inference(step,[status(thm)],[t43,t38]) ).
cnf(t1496,plain,
true = ifeq(c_lessequals(X1,c_plus(X2,X1,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true),
inference(step,[status(thm)],[t1495,t22]) ).
cnf(t629,plain,
ifeq(c_lessequals(X1,c_plus(X2,X1,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true) = true,
inference(orient,[status(thm)],[t1496]) ).
cnf(t637,plain,
true = ifeq(c_lessequals(X1,c_plus(X1,X2,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true),
inference(cp,[status(thm)],[t629,t156]) ).
cnf(t667,plain,
ifeq(c_lessequals(X1,c_plus(X1,X2,t_b),t_b),true,c_lessequals(c_0,X2,t_b),true) = true,
inference(orient,[status(thm)],[t637]) ).
cnf(t669,plain,
true = ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_0,c_minus(X2,X1,t_b),t_b),true),
inference(cp,[status(thm)],[t667,t104]) ).
cnf(t703,plain,
ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_0,c_minus(X2,X1,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t669]) ).
cnf(f7,negated_conjecture,
c_lessequals(v_g(V_U),v_k(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f7_nnf,plain,
! [V_U] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_U] : c_lessequals(v_g(V_U),v_k(V_U),t_b),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
c_lessequals(v_g(X0),v_k(X0),t_b),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t7,plain,
c_lessequals(v_g(X1),v_k(X1),t_b) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t34,plain,
c_lessequals(v_g(X1),v_k(X1),t_b) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t704,plain,
true = ifeq(true,true,c_lessequals(c_0,c_minus(v_k(X1),v_g(X1),t_b),t_b),true),
inference(cp,[status(thm)],[t703,t34]) ).
cnf(t1499,plain,
true = c_lessequals(c_0,c_minus(v_k(X1),v_g(X1),t_b),t_b),
inference(step,[status(thm)],[t704,t22]) ).
cnf(t714,plain,
c_lessequals(c_0,c_minus(v_k(X1),v_g(X1),t_b),t_b) = true,
inference(orient,[status(thm)],[t1499]) ).
cnf(t1166,plain,
true = ifeq(true,true,c_lessequals(c_plus(c_0,c_minus(X1,c_minus(v_k(X2),v_g(X2),t_b),t_b),t_b),X1,t_b),true),
inference(cp,[status(thm)],[t1165,t714]) ).
cnf(t1522,plain,
true = c_lessequals(c_plus(c_0,c_minus(X1,c_minus(v_k(X2),v_g(X2),t_b),t_b),t_b),X1,t_b),
inference(step,[status(thm)],[t1166,t22]) ).
cnf(t1523,plain,
true = c_lessequals(c_minus(X1,c_minus(v_k(X2),v_g(X2),t_b),t_b),X1,t_b),
inference(step,[status(thm)],[t1522,t21]) ).
cnf(t1524,plain,
true = c_lessequals(c_plus(X1,c_minus(v_g(X2),v_k(X2),t_b),t_b),X1,t_b),
inference(step,[status(thm)],[t1523,t66]) ).
cnf(t1192,plain,
c_lessequals(c_plus(X1,c_minus(v_g(X2),v_k(X2),t_b),t_b),X1,t_b) = true,
inference(orient,[status(thm)],[t1524]) ).
cnf(t1197,plain,
true = ifeq(true,true,c_lessequals(X1,c_minus(X1,c_minus(v_g(X2),v_k(X2),t_b),t_b),t_b),true),
inference(cp,[status(thm)],[t1134,t1192]) ).
cnf(t1526,plain,
true = c_lessequals(X1,c_minus(X1,c_minus(v_g(X2),v_k(X2),t_b),t_b),t_b),
inference(step,[status(thm)],[t1197,t22]) ).
cnf(t1527,plain,
true = c_lessequals(X1,c_plus(X1,c_minus(v_k(X2),v_g(X2),t_b),t_b),t_b),
inference(step,[status(thm)],[t1526,t66]) ).
cnf(t1203,plain,
c_lessequals(X1,c_plus(X1,c_minus(v_k(X2),v_g(X2),t_b),t_b),t_b) = true,
inference(orient,[status(thm)],[t1527]) ).
cnf(hi2,axiom,
ifeq(class_OrderedGroup_Oab__group__add(X0),true,c_plus(c_minus(X1,X2,X0),X3,X0),c_minus(c_plus(X1,X3,X0),X2,X0)) = c_minus(c_plus(X1,X3,X0),X2,X0),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
c_plus(c_minus(X1,X2,t_b),X3,t_b) = c_minus(c_plus(X1,X3,t_b),X2,t_b),
inference(hyper_resolution,[status(thm)],[hi2,h1]) ).
cnf(t1454,plain,
c_plus(c_minus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X3,X2,t_b),t_b),
inference(step,[status(thm)],[t15,t67]) ).
cnf(t79,plain,
c_plus(c_minus(X1,X2,t_b),X3,t_b) = c_plus(X1,c_minus(X3,X2,t_b),t_b),
inference(orient,[status(thm)],[t1454]) ).
cnf(t157,plain,
c_plus(X1,c_minus(X2,X3,t_b),t_b) = c_plus(X2,c_minus(X1,X3,t_b),t_b),
inference(cp,[status(thm)],[t156,t79]) ).
cnf(t230,plain,
c_plus(X1,c_minus(X2,X3,t_b),t_b) = c_plus(X2,c_minus(X1,X3,t_b),t_b),
inference(orient,[status(thm)],[t157]) ).
cnf(t1206,plain,
true = c_lessequals(X1,c_plus(v_k(X2),c_minus(X1,v_g(X2),t_b),t_b),t_b),
inference(cp,[status(thm)],[t1203,t230]) ).
cnf(t1208,plain,
c_lessequals(X1,c_plus(v_k(X2),c_minus(X1,v_g(X2),t_b),t_b),t_b) = true,
inference(orient,[status(thm)],[t1206]) ).
cnf(t1416,plain,
true = ifeq(true,true,c_lessequals(c_minus(X1,v_k(X2),t_b),c_minus(X1,v_g(X2),t_b),t_b),true),
inference(cp,[status(thm)],[t1415,t1208]) ).
cnf(t1541,plain,
true = c_lessequals(c_minus(X1,v_k(X2),t_b),c_minus(X1,v_g(X2),t_b),t_b),
inference(step,[status(thm)],[t1416,t22]) ).
cnf(t1446,plain,
c_lessequals(c_minus(X1,v_k(X2),t_b),c_minus(X1,v_g(X2),t_b),t_b) = true,
inference(orient,[status(thm)],[t1541]) ).
cnf(f8,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8_nnf,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1446]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 05:47:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.94/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.94/1.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------