%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 12:55:04 PM UTC 2026
% Result : Unsatisfiable 3.58s 0.84s
% Output : Proof 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 105 ( 65 unt; 0 def)
% Number of atoms : 149 ( 77 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 130 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t28,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f11,axiom,
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f11_nnf,plain,
! [T] :
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [T] :
( class_Ring__and__Field_Oordered__idom(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi9,axiom,
ifeq(class_Ring__and__Field_Oordered__field(X0),true,class_Ring__and__Field_Oordered__idom(X0),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f2,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f2_nnf,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi0,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
class_Ring__and__Field_Oordered__idom(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi0]) ).
cnf(f6,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,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)],[f6_sk]) ).
cnf(hi4,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)],[c6]) ).
cnf(t25,plain,
c_times(c_HOL_Oabs(X1,t_a),c_HOL_Oabs(X2,t_a),t_a) = c_HOL_Oabs(c_times(X1,X2,t_a),t_a),
inference(hyper_resolution,[status(thm)],[hi4,h1]) ).
cnf(t77,plain,
c_times(c_HOL_Oabs(X1,t_a),c_HOL_Oabs(X2,t_a),t_a) = c_HOL_Oabs(c_times(X1,X2,t_a),t_a),
inference(orient,[status(thm)],[t25]) ).
cnf(t119,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_HOL_Oabs(c_times(v_c,v_f(v_x(X1)),t_a),t_a),t_a),t_a) = false,
inference(step,[status(thm)],[t28,t77]) ).
cnf(t85,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_HOL_Oabs(c_times(v_c,v_f(v_x(X1)),t_a),t_a),t_a),t_a) = false,
inference(orient,[status(thm)],[t119]) ).
cnf(t86,plain,
false = c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),c_HOL_Oabs(c_times(X1,c_times(v_c,v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),t_a),t_a),t_a),
inference(cp,[status(thm)],[t85,t77]) ).
cnf(t101,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),c_HOL_Oabs(c_times(X1,c_times(v_c,v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),t_a),t_a),t_a) = false,
inference(orient,[status(thm)],[t86]) ).
cnf(f10,axiom,
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f10_nnf,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi8,axiom,
ifeq(class_Ring__and__Field_Oordered__field(X0),true,class_Ring__and__Field_Ofield(X0),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h2,plain,
class_Ring__and__Field_Ofield(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi0]) ).
cnf(f9,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f9_nnf,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi7,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,class_OrderedGroup_Osemigroup__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h5,plain,
class_OrderedGroup_Osemigroup__mult(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi7,h2]) ).
cnf(f4,axiom,
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f4_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( 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,[status(esa)],[f4_sk]) ).
cnf(hi2,axiom,
ifeq(class_OrderedGroup_Osemigroup__mult(X0),true,c_times(c_times(X1,X2,X0),X3,X0),c_times(X1,c_times(X2,X3,X0),X0)) = c_times(X1,c_times(X2,X3,X0),X0),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t26,plain,
c_times(c_times(X1,X2,t_a),X3,t_a) = c_times(X1,c_times(X2,X3,t_a),t_a),
inference(hyper_resolution,[status(thm)],[hi2,h5]) ).
cnf(t71,plain,
c_times(c_times(X1,X2,t_a),X3,t_a) = c_times(X1,c_times(X2,X3,t_a),t_a),
inference(orient,[status(thm)],[t26]) ).
cnf(t21,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(f7,axiom,
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f7_nnf,plain,
! [T_a,V_a] :
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T_a,V_a] :
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,or(eq(X1,c_0),eq(c_times(c_HOL_Oinverse(X1,X0),X1,X0),c_1)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t24,plain,
or(eq(X1,c_0),eq(c_times(c_HOL_Oinverse(X1,t_a),X1,t_a),c_1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2]) ).
cnf(t53,plain,
or(eq(X1,c_0),eq(c_times(c_HOL_Oinverse(X1,t_a),X1,t_a),c_1)) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(f0,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
v_c != c_0,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
v_c != c_0,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
v_c != c_0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t7,plain,
eq(v_c,c_0) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t81,plain,
eq(v_c,c_0) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t83,plain,
true = or(false,eq(c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a),c_1)),
inference(cp,[status(thm)],[t53,t81]) ).
cnf(t10,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t38,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t120,plain,
true = eq(c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a),c_1),
inference(step,[status(thm)],[t83,t38]) ).
cnf(t90,plain,
eq(c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a),c_1) = true,
inference(orient,[status(thm)],[t120]) ).
cnf(t91,plain,
c_1 = ifeq(true,true,c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a),c_1),
inference(cp,[status(thm)],[t34,t90]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t121,plain,
c_1 = c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a),
inference(step,[status(thm)],[t91,t33]) ).
cnf(t92,plain,
c_times(c_HOL_Oinverse(v_c,t_a),v_c,t_a) = c_1,
inference(orient,[status(thm)],[t121]) ).
cnf(t93,plain,
c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,X1,t_a),t_a) = c_times(c_1,X1,t_a),
inference(cp,[status(thm)],[t71,t92]) ).
cnf(f8,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
fof(f8_nnf,plain,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,class_OrderedGroup_Omonoid__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h6,plain,
class_OrderedGroup_Omonoid__mult(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi6,h2]) ).
cnf(f3,axiom,
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f3_nnf,plain,
! [T_a,V_y] :
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_y] :
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_times(c_1,X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi1,axiom,
ifeq(class_OrderedGroup_Omonoid__mult(X0),true,c_times(c_1,X1,X0),X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t13,plain,
c_times(c_1,X1,t_a) = X1,
inference(hyper_resolution,[status(thm)],[hi1,h6]) ).
cnf(t32,plain,
c_times(c_1,X1,t_a) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t122,plain,
c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,X1,t_a),t_a) = X1,
inference(step,[status(thm)],[t93,t32]) ).
cnf(t95,plain,
c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,X1,t_a),t_a) = X1,
inference(orient,[status(thm)],[t122]) ).
cnf(t102,plain,
false = c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),
inference(cp,[status(thm)],[t101,t95]) ).
cnf(f12,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f12_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi10,axiom,
ifeq(class_Ring__and__Field_Oordered__field(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h0,plain,
class_Orderings_Oorder(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi0]) ).
cnf(f5,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f5_nnf,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi3,axiom,
ifeq(class_Orderings_Oorder(X0),true,c_lessequals(X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t12,plain,
c_lessequals(X1,X1,t_a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(t62,plain,
c_lessequals(X1,X1,t_a) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t126,plain,
false = true,
inference(step,[status(thm)],[t102,t62]) ).
cnf(t105,plain,
false = true,
inference(orient,[status(thm)],[t126]) ).
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,t105]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 25 05:44:50 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.58/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/0.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------