%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 12:55:08 PM UTC 2026
% Result : Unsatisfiable 16.21s 2.67s
% Output : Proof 16.21s
% 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(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c2,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)],[f2_sk]) ).
cnf(t18,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)],[c2]) ).
cnf(t28,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)],[t18]) ).
cnf(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f0_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)],[c0]) ).
cnf(t26,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(f10,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(f10_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t8,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t24,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f11_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t0,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t36,plain,
true = ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true),
inference(cp,[status(thm)],[t24,t35]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t152,plain,
true = class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(step,[status(thm)],[t36,t19]) ).
cnf(t57,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(orient,[status(thm)],[t152]) ).
cnf(t59,plain,
true = ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),true),
inference(cp,[status(thm)],[t26,t57]) ).
cnf(t156,plain,
true = c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),
inference(step,[status(thm)],[t59,t19]) ).
cnf(t69,plain,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b) = true,
inference(orient,[status(thm)],[t156]) ).
cnf(t74,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)],[t28,t69]) ).
cnf(f9,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(f9_nnf,plain,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_Orderings_Olinorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t9,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t25,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t37,plain,
true = ifeq(true,true,class_Orderings_Olinorder(t_b),true),
inference(cp,[status(thm)],[t25,t35]) ).
cnf(t153,plain,
true = class_Orderings_Olinorder(t_b),
inference(step,[status(thm)],[t37,t19]) ).
cnf(t60,plain,
class_Orderings_Olinorder(t_b) = true,
inference(orient,[status(thm)],[t153]) ).
cnf(t183,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)],[t74,t60]) ).
cnf(t184,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)],[t183,t19]) ).
cnf(t185,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)],[t184,t19]) ).
cnf(t134,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)],[t185]) ).
cnf(f6,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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(f6_nnf,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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)],[f6]) ).
fof(f6_sk,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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)],[f6_nnf]) ).
cnf(c6,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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)],[f6_sk]) ).
cnf(t15,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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)],[c6]) ).
cnf(t47,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(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(t138,plain,
true = ifeq(c_lessequals(c_minus(v_k(v_x),v_g(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)],[t134,t47]) ).
cnf(f3,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(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(t17,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)],[c3]) ).
cnf(t30,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)],[t17]) ).
cnf(t71,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)],[t30,t69]) ).
cnf(f7,axiom,
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f7_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_LOrder_Ojoin__semilorder(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t6,plain,
ifeq(class_LOrder_Ojoin__semilorder(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t32,plain,
ifeq(class_LOrder_Ojoin__semilorder(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f8,axiom,
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f8_nnf,plain,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_LOrder_Ojoin__semilorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_LOrder_Ojoin__semilorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t27,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_LOrder_Ojoin__semilorder(X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t58,plain,
true = ifeq(true,true,class_LOrder_Ojoin__semilorder(t_b),true),
inference(cp,[status(thm)],[t27,t57]) ).
cnf(t154,plain,
true = class_LOrder_Ojoin__semilorder(t_b),
inference(step,[status(thm)],[t58,t19]) ).
cnf(t63,plain,
class_LOrder_Ojoin__semilorder(t_b) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t64,plain,
true = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(cp,[status(thm)],[t32,t63]) ).
cnf(t155,plain,
true = class_Orderings_Oorder(t_b),
inference(step,[status(thm)],[t64,t19]) ).
cnf(t65,plain,
class_Orderings_Oorder(t_b) = true,
inference(orient,[status(thm)],[t155]) ).
cnf(t165,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)],[t71,t65]) ).
cnf(t166,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)],[t165,t19]) ).
cnf(t167,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)],[t166,t19]) ).
cnf(t91,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)],[t167]) ).
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f4_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)],[c4]) ).
cnf(t31,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(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f1_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)],[c1]) ).
cnf(t29,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(t61,plain,
true = ifeq(true,true,or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)),true),
inference(cp,[status(thm)],[t29,t60]) ).
cnf(t157,plain,
true = or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)),
inference(step,[status(thm)],[t61,t19]) ).
cnf(t76,plain,
or(c_less(X1,X2,t_b),c_lessequals(X2,X1,t_b)) = true,
inference(orient,[status(thm)],[t157]) ).
cnf(f5,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5_nnf,plain,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t38,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t77,plain,
true = or(c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),false),
inference(cp,[status(thm)],[t76,t38]) ).
cnf(t1,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t20,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t158,plain,
true = c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(step,[status(thm)],[t77,t20]) ).
cnf(t79,plain,
c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t80,plain,
true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(true,true,c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),true),true),
inference(cp,[status(thm)],[t31,t79]) ).
cnf(t159,plain,
true = ifeq(true,true,ifeq(true,true,c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),true),true),
inference(step,[status(thm)],[t80,t65]) ).
cnf(t160,plain,
true = ifeq(true,true,c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),true),
inference(step,[status(thm)],[t159,t19]) ).
cnf(t161,plain,
true = c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(step,[status(thm)],[t160,t19]) ).
cnf(t81,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) = true,
inference(orient,[status(thm)],[t161]) ).
cnf(t92,plain,
true = ifeq(true,true,c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b),true),
inference(cp,[status(thm)],[t91,t81]) ).
cnf(t168,plain,
true = c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(step,[status(thm)],[t92,t19]) ).
cnf(t96,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X1,t_b),t_b) = true,
inference(orient,[status(thm)],[t168]) ).
cnf(t186,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t138,t96]) ).
cnf(t187,plain,
true = false,
inference(step,[status(thm)],[t186,t19]) ).
cnf(t139,plain,
false = true,
inference(orient,[status(thm)],[t187]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t139]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:50:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.21/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.21/2.67 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------