%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 12:55:06 PM UTC 2026
% Result : Unsatisfiable 12.84s 2.18s
% Output : Proof 12.84s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t12,axiom,
sFlat0 = v_f(v_x),
introduced(definition) ).
cnf(f0,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
v_f(c_0) = c_0,
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
v_f(c_0) = c_0,
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t2,plain,
v_f(c_0) = c_0,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f2,negated_conjecture,
v_x = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f2_nnf,plain,
v_x = c_0,
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
v_x = c_0,
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t0,plain,
v_x = c_0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t32,plain,
c_0 = v_x,
inference(orient,[status(thm)],[t0]) ).
cnf(t141,plain,
v_f(v_x) = c_0,
inference(step,[status(thm)],[t2,t32]) ).
cnf(t142,plain,
v_f(v_x) = v_x,
inference(step,[status(thm)],[t141,t32]) ).
cnf(t37,plain,
v_f(v_x) = v_x,
inference(orient,[status(thm)],[t142]) ).
cnf(t147,plain,
sFlat0 = v_x,
inference(step,[status(thm)],[t12,t37]) ).
cnf(t42,plain,
v_x = sFlat0,
inference(orient,[status(thm)],[t147]) ).
cnf(t151,plain,
v_f(sFlat0) = v_x,
inference(step,[status(thm)],[t37,t42]) ).
cnf(t152,plain,
v_f(sFlat0) = sFlat0,
inference(step,[status(thm)],[t151,t42]) ).
cnf(t46,plain,
v_f(sFlat0) = sFlat0,
inference(rw,[status(thm)],[t152]) ).
cnf(t54,plain,
v_f(sFlat0) = sFlat0,
inference(orient,[status(thm)],[t46]) ).
cnf(t13,axiom,
sFlat1 = c_HOL_Oabs(v_f(v_x),t_a),
introduced(definition) ).
cnf(t143,plain,
sFlat1 = c_HOL_Oabs(v_x,t_a),
inference(step,[status(thm)],[t13,t37]) ).
cnf(t38,plain,
c_HOL_Oabs(v_x,t_a) = sFlat1,
inference(orient,[status(thm)],[t143]) ).
cnf(t150,plain,
c_HOL_Oabs(sFlat0,t_a) = sFlat1,
inference(step,[status(thm)],[t38,t42]) ).
cnf(t45,plain,
c_HOL_Oabs(sFlat0,t_a) = sFlat1,
inference(rw,[status(thm)],[t150]) ).
cnf(t55,plain,
c_HOL_Oabs(sFlat0,t_a) = sFlat1,
inference(orient,[status(thm)],[t45]) ).
cnf(f5,axiom,
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f5_nnf,plain,
! [T_a] :
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a] :
( c_HOL_Oabs(c_0,T_a) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_HOL_Oabs(c_0,X0) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t8,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(c_0,X1),c_0) = c_0,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t31,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(c_0,X1),c_0) = c_0,
inference(orient,[status(thm)],[t8]) ).
cnf(t134,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(v_x,X1),c_0) = c_0,
inference(step,[status(thm)],[t31,t32]) ).
cnf(t135,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(v_x,X1),v_x) = c_0,
inference(step,[status(thm)],[t134,t32]) ).
cnf(t136,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(v_x,X1),v_x) = v_x,
inference(step,[status(thm)],[t135,t32]) ).
cnf(t34,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(v_x,X1),v_x) = v_x,
inference(rw,[status(thm)],[t136]) ).
cnf(t167,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(sFlat0,X1),v_x) = v_x,
inference(step,[status(thm)],[t34,t42]) ).
cnf(t168,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(sFlat0,X1),sFlat0) = v_x,
inference(step,[status(thm)],[t167,t42]) ).
cnf(t169,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(sFlat0,X1),sFlat0) = sFlat0,
inference(step,[status(thm)],[t168,t42]) ).
cnf(t65,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_HOL_Oabs(sFlat0,X1),sFlat0) = sFlat0,
inference(orient,[status(thm)],[t169]) ).
cnf(f11,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(f11_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t5,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t19,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f4,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t1,plain,
class_Ring__and__Field_Oordered__idom(t_a) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t25,plain,
class_Ring__and__Field_Oordered__idom(t_a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t26,plain,
true = ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_a),true),
inference(cp,[status(thm)],[t19,t25]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t157,plain,
true = class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(step,[status(thm)],[t26,t18]) ).
cnf(t50,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a) = true,
inference(orient,[status(thm)],[t157]) ).
cnf(t66,plain,
sFlat0 = ifeq(true,true,c_HOL_Oabs(sFlat0,t_a),sFlat0),
inference(cp,[status(thm)],[t65,t50]) ).
cnf(t170,plain,
sFlat0 = c_HOL_Oabs(sFlat0,t_a),
inference(step,[status(thm)],[t66,t18]) ).
cnf(t171,plain,
sFlat0 = sFlat1,
inference(step,[status(thm)],[t170,t55]) ).
cnf(t68,plain,
sFlat1 = sFlat0,
inference(orient,[status(thm)],[t171]) ).
cnf(t172,plain,
c_HOL_Oabs(sFlat0,t_a) = sFlat0,
inference(step,[status(thm)],[t55,t68]) ).
cnf(t69,plain,
c_HOL_Oabs(sFlat0,t_a) = sFlat0,
inference(orient,[status(thm)],[t172]) ).
cnf(t14,axiom,
sFlat2 = v_h(v_x),
introduced(definition) ).
cnf(t154,plain,
sFlat2 = v_h(sFlat0),
inference(step,[status(thm)],[t14,t42]) ).
cnf(t48,plain,
v_h(sFlat0) = sFlat2,
inference(orient,[status(thm)],[t154]) ).
cnf(t15,axiom,
sFlat3 = c_HOL_Oabs(v_h(v_x),t_a),
introduced(definition) ).
cnf(t39,plain,
c_HOL_Oabs(v_h(v_x),t_a) = sFlat3,
inference(orient,[status(thm)],[t15]) ).
cnf(t153,plain,
c_HOL_Oabs(v_h(sFlat0),t_a) = sFlat3,
inference(step,[status(thm)],[t39,t42]) ).
cnf(t47,plain,
c_HOL_Oabs(v_h(sFlat0),t_a) = sFlat3,
inference(rw,[status(thm)],[t153]) ).
cnf(t161,plain,
c_HOL_Oabs(sFlat2,t_a) = sFlat3,
inference(step,[status(thm)],[t47,t48]) ).
cnf(t58,plain,
c_HOL_Oabs(sFlat2,t_a) = sFlat3,
inference(orient,[status(thm)],[t161]) ).
cnf(t16,axiom,
sFlat4 = c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),
introduced(definition) ).
cnf(t155,plain,
sFlat4 = c_times(v_c,c_HOL_Oabs(v_h(sFlat0),t_a),t_a),
inference(step,[status(thm)],[t16,t42]) ).
cnf(t156,plain,
sFlat4 = c_times(v_c,c_HOL_Oabs(sFlat2,t_a),t_a),
inference(step,[status(thm)],[t155,t48]) ).
cnf(t49,plain,
c_times(v_c,c_HOL_Oabs(sFlat2,t_a),t_a) = sFlat4,
inference(orient,[status(thm)],[t156]) ).
cnf(t162,plain,
c_times(v_c,sFlat3,t_a) = sFlat4,
inference(step,[status(thm)],[t49,t58]) ).
cnf(t59,plain,
c_times(v_c,sFlat3,t_a) = sFlat4,
inference(rw,[status(thm)],[t162]) ).
cnf(t61,plain,
c_times(v_c,sFlat3,t_a) = sFlat4,
inference(orient,[status(thm)],[t59]) ).
cnf(t17,axiom,
sFlat5 = c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
introduced(definition) ).
cnf(t144,plain,
sFlat5 = c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(step,[status(thm)],[t17,t37]) ).
cnf(t145,plain,
sFlat5 = c_lessequals(sFlat1,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(step,[status(thm)],[t144,t38]) ).
cnf(t146,plain,
sFlat5 = c_lessequals(sFlat1,c_times(v_c,sFlat3,t_a),t_a),
inference(step,[status(thm)],[t145,t39]) ).
cnf(t40,plain,
c_lessequals(sFlat1,c_times(v_c,sFlat3,t_a),t_a) = sFlat5,
inference(orient,[status(thm)],[t146]) ).
cnf(t166,plain,
c_lessequals(sFlat1,sFlat4,t_a) = sFlat5,
inference(step,[status(thm)],[t40,t61]) ).
cnf(t62,plain,
c_lessequals(sFlat1,sFlat4,t_a) = sFlat5,
inference(rw,[status(thm)],[t166]) ).
cnf(t63,plain,
c_lessequals(sFlat1,sFlat4,t_a) = sFlat5,
inference(orient,[status(thm)],[t62]) ).
cnf(t174,plain,
c_lessequals(sFlat0,sFlat4,t_a) = sFlat5,
inference(step,[status(thm)],[t63,t68]) ).
cnf(t71,plain,
c_lessequals(sFlat0,sFlat4,t_a) = sFlat5,
inference(rw,[status(thm)],[t174]) ).
cnf(t72,plain,
c_lessequals(sFlat0,sFlat4,t_a) = sFlat5,
inference(orient,[status(thm)],[t71]) ).
cnf(f8,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(f8_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)],[f8]) ).
fof(f8_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)],[f8_nnf]) ).
cnf(c8,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)],[f8_sk]) ).
cnf(t11,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t24,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t138,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(v_x,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t24,t32]) ).
cnf(t139,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(v_x,X2,X1),true,ifeq(c_lessequals(v_x,X3,X1),true,c_lessequals(c_0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t138,t32]) ).
cnf(t140,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(v_x,X2,X1),true,ifeq(c_lessequals(v_x,X3,X1),true,c_lessequals(v_x,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t139,t32]) ).
cnf(t36,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(v_x,X2,X1),true,ifeq(c_lessequals(v_x,X3,X1),true,c_lessequals(v_x,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(rw,[status(thm)],[t140]) ).
cnf(t190,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(sFlat0,X2,X1),true,ifeq(c_lessequals(v_x,X3,X1),true,c_lessequals(v_x,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t36,t42]) ).
cnf(t191,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(sFlat0,X2,X1),true,ifeq(c_lessequals(sFlat0,X3,X1),true,c_lessequals(v_x,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t190,t42]) ).
cnf(t192,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(sFlat0,X2,X1),true,ifeq(c_lessequals(sFlat0,X3,X1),true,c_lessequals(sFlat0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(step,[status(thm)],[t191,t42]) ).
cnf(t89,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(sFlat0,X2,X1),true,ifeq(c_lessequals(sFlat0,X3,X1),true,c_lessequals(sFlat0,c_times(X3,X2,X1),X1),true),true),true) = true,
inference(orient,[status(thm)],[t192]) ).
cnf(t101,plain,
true = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_a),true,ifeq(c_lessequals(sFlat0,sFlat3,t_a),true,ifeq(c_lessequals(sFlat0,v_c,t_a),true,c_lessequals(sFlat0,sFlat4,t_a),true),true),true),
inference(cp,[status(thm)],[t89,t61]) ).
cnf(f9,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(f9_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t21,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t27,plain,
true = ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_a),true),
inference(cp,[status(thm)],[t21,t25]) ).
cnf(t158,plain,
true = class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(step,[status(thm)],[t27,t18]) ).
cnf(t51,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t193,plain,
true = ifeq(true,true,ifeq(c_lessequals(sFlat0,sFlat3,t_a),true,ifeq(c_lessequals(sFlat0,v_c,t_a),true,c_lessequals(sFlat0,sFlat4,t_a),true),true),true),
inference(step,[status(thm)],[t101,t51]) ).
cnf(t194,plain,
true = ifeq(c_lessequals(sFlat0,sFlat3,t_a),true,ifeq(c_lessequals(sFlat0,v_c,t_a),true,c_lessequals(sFlat0,sFlat4,t_a),true),true),
inference(step,[status(thm)],[t193,t18]) ).
cnf(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t9,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)],[c6]) ).
cnf(t22,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)],[t9]) ).
cnf(t137,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(v_x,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(step,[status(thm)],[t22,t32]) ).
cnf(t35,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(v_x,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(rw,[status(thm)],[t137]) ).
cnf(t177,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(sFlat0,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(step,[status(thm)],[t35,t42]) ).
cnf(t75,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(sFlat0,c_HOL_Oabs(X2,X1),X1),true) = true,
inference(orient,[status(thm)],[t177]) ).
cnf(t78,plain,
true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(t_a),true,c_lessequals(sFlat0,sFlat3,t_a),true),
inference(cp,[status(thm)],[t75,t58]) ).
cnf(t180,plain,
true = ifeq(true,true,c_lessequals(sFlat0,sFlat3,t_a),true),
inference(step,[status(thm)],[t78,t50]) ).
cnf(t181,plain,
true = c_lessequals(sFlat0,sFlat3,t_a),
inference(step,[status(thm)],[t180,t18]) ).
cnf(t81,plain,
c_lessequals(sFlat0,sFlat3,t_a) = true,
inference(orient,[status(thm)],[t181]) ).
cnf(t195,plain,
true = ifeq(true,true,ifeq(c_lessequals(sFlat0,v_c,t_a),true,c_lessequals(sFlat0,sFlat4,t_a),true),true),
inference(step,[status(thm)],[t194,t81]) ).
cnf(t196,plain,
true = ifeq(c_lessequals(sFlat0,v_c,t_a),true,c_lessequals(sFlat0,sFlat4,t_a),true),
inference(step,[status(thm)],[t195,t18]) ).
cnf(f7,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(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,plain,
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t10,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)],[c7]) ).
cnf(t23,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)],[t10]) ).
cnf(f1,negated_conjecture,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_less(c_0,v_c,t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_less(c_0,v_c,t_a),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t3,plain,
c_less(c_0,v_c,t_a) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t29,plain,
c_less(c_0,v_c,t_a) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t133,plain,
c_less(v_x,v_c,t_a) = true,
inference(step,[status(thm)],[t29,t32]) ).
cnf(t33,plain,
c_less(v_x,v_c,t_a) = true,
inference(rw,[status(thm)],[t133]) ).
cnf(t160,plain,
c_less(sFlat0,v_c,t_a) = true,
inference(step,[status(thm)],[t33,t42]) ).
cnf(t56,plain,
c_less(sFlat0,v_c,t_a) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t57,plain,
true = ifeq(class_Orderings_Oorder(t_a),true,ifeq(true,true,c_lessequals(sFlat0,v_c,t_a),true),true),
inference(cp,[status(thm)],[t23,t56]) ).
cnf(f10,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f10_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t6,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t20,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Oorder(X1),true) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t28,plain,
true = ifeq(true,true,class_Orderings_Oorder(t_a),true),
inference(cp,[status(thm)],[t20,t25]) ).
cnf(t159,plain,
true = class_Orderings_Oorder(t_a),
inference(step,[status(thm)],[t28,t18]) ).
cnf(t52,plain,
class_Orderings_Oorder(t_a) = true,
inference(orient,[status(thm)],[t159]) ).
cnf(t163,plain,
true = ifeq(true,true,ifeq(true,true,c_lessequals(sFlat0,v_c,t_a),true),true),
inference(step,[status(thm)],[t57,t52]) ).
cnf(t164,plain,
true = ifeq(true,true,c_lessequals(sFlat0,v_c,t_a),true),
inference(step,[status(thm)],[t163,t18]) ).
cnf(t165,plain,
true = c_lessequals(sFlat0,v_c,t_a),
inference(step,[status(thm)],[t164,t18]) ).
cnf(t60,plain,
c_lessequals(sFlat0,v_c,t_a) = true,
inference(orient,[status(thm)],[t165]) ).
cnf(t197,plain,
true = ifeq(true,true,c_lessequals(sFlat0,sFlat4,t_a),true),
inference(step,[status(thm)],[t196,t60]) ).
cnf(t198,plain,
true = c_lessequals(sFlat0,sFlat4,t_a),
inference(step,[status(thm)],[t197,t18]) ).
cnf(t199,plain,
true = sFlat5,
inference(step,[status(thm)],[t198,t72]) ).
cnf(t102,plain,
true = sFlat5,
inference(orient,[status(thm)],[t199]) ).
cnf(f3,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3_nnf,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
c_lessequals(c_HOL_Oabs(v_f(sFlat0),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) != true,
inference(rw,[status(thm)],[goal_0,t42]) ).
cnf(g0_1,plain,
c_lessequals(c_HOL_Oabs(sFlat0,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) != true,
inference(rw,[status(thm)],[g0_0,t54]) ).
cnf(g0_2,plain,
c_lessequals(sFlat0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) != true,
inference(rw,[status(thm)],[g0_1,t69]) ).
cnf(g0_3,plain,
c_lessequals(sFlat0,c_times(v_c,c_HOL_Oabs(v_h(sFlat0),t_a),t_a),t_a) != true,
inference(rw,[status(thm)],[g0_2,t42]) ).
cnf(g0_4,plain,
c_lessequals(sFlat0,c_times(v_c,c_HOL_Oabs(sFlat2,t_a),t_a),t_a) != true,
inference(rw,[status(thm)],[g0_3,t48]) ).
cnf(g0_5,plain,
c_lessequals(sFlat0,c_times(v_c,sFlat3,t_a),t_a) != true,
inference(rw,[status(thm)],[g0_4,t58]) ).
cnf(g0_6,plain,
c_lessequals(sFlat0,sFlat4,t_a) != true,
inference(rw,[status(thm)],[g0_5,t61]) ).
cnf(g0_7,plain,
sFlat5 != true,
inference(rw,[status(thm)],[g0_6,t72]) ).
cnf(g0_8,plain,
sFlat5 != sFlat5,
inference(rw,[status(thm)],[g0_7,t102]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.53 % Computer : n020.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Fri Sep 25 05:47:04 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.84/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.84/2.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------