%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 12:02:32 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n026.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Mon Sep 21 13:27:29 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 0.16/5.48 % Refutation found
% 0.16/5.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% 0.16/5.48 fof(f1,negated_conjecture,(
% 0.16/5.48 c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f2,negated_conjecture,(
% 0.16/5.48 c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f3,negated_conjecture,(
% 0.16/5.48 ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f4,negated_conjecture,(
% 0.16/5.48 class_Ring__and__Field_Oordered__idom(t_b) ),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f5,axiom,(
% 0.16/5.48 (![T_a,V_y]: (( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)| c_plus(c_0,V_y,T_a) = V_y ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f6,axiom,(
% 0.16/5.48 (![T_a,V_a,V_c,V_b]: (( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)| ~ 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) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f7,axiom,(
% 0.16/5.48 (![T_a,V_a,V_b,V_c]: (( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f8,axiom,(
% 0.16/5.48 (![T_a,V_y,V_z,V_x]: (( ~ class_Orderings_Oorder(T_a)| ~ c_lessequals(V_y,V_z,T_a)| ~ c_lessequals(V_x,V_y,T_a)| c_lessequals(V_x,V_z,T_a) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f9,axiom,(
% 0.16/5.48 (![T]: (( ~ class_LOrder_Ojoin__semilorder(T)| class_Orderings_Oorder(T) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f10,axiom,(
% 0.16/5.48 (![T]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T)| class_OrderedGroup_Opordered__ab__group__add(T) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f11,axiom,(
% 0.16/5.48 (![T]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T)| class_LOrder_Ojoin__semilorder(T) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f12,axiom,(
% 0.16/5.48 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_OrderedGroup_Ocomm__monoid__add(T) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f13,axiom,(
% 0.16/5.48 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_OrderedGroup_Olordered__ab__group__abs(T) ) ))),
% 0.16/5.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f14,plain,(
% 0.16/5.48 c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.16/5.48 fof(f15,plain,(
% 0.16/5.48 c_lessequals(v_g(v_x),v_k(v_x),t_b)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f2])).
% 0.16/5.48 fof(f16,plain,(
% 0.16/5.48 ~c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.16/5.48 fof(f17,plain,(
% 0.16/5.48 class_Ring__and__Field_Oordered__idom(t_b)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.16/5.48 fof(f18,plain,(
% 0.16/5.48 ![T_a]: (~class_OrderedGroup_Ocomm__monoid__add(T_a)|(![V_y]: c_plus(c_0,V_y,T_a)=V_y))),
% 0.16/5.49 inference(miniscoping,[status(thm)],[f5])).
% 0.16/5.49 fof(f19,plain,(
% 0.16/5.49 ![X0,X1]: (~class_OrderedGroup_Ocomm__monoid__add(X0)|c_plus(c_0,X1,X0)=X1)),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f18])).
% 0.16/5.49 fof(f20,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~class_OrderedGroup_Opordered__ab__group__add(X0)|~c_lessequals(X1,c_minus(X2,X3,X0),X0)|c_lessequals(c_plus(X1,X3,X0),X2,X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f6])).
% 0.16/5.49 fof(f21,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~class_OrderedGroup_Opordered__ab__group__add(X0)|~c_lessequals(c_plus(X1,X2,X0),X3,X0)|c_lessequals(X1,c_minus(X3,X2,X0),X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f7])).
% 0.16/5.49 fof(f22,plain,(
% 0.16/5.49 ![T_a,V_z,V_x]: ((![V_y]: ((~class_Orderings_Oorder(T_a)|~c_lessequals(V_y,V_z,T_a))|~c_lessequals(V_x,V_y,T_a)))|c_lessequals(V_x,V_z,T_a))),
% 0.16/5.49 inference(miniscoping,[status(thm)],[f8])).
% 0.16/5.49 fof(f23,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~class_Orderings_Oorder(X0)|~c_lessequals(X1,X2,X0)|~c_lessequals(X3,X1,X0)|c_lessequals(X3,X2,X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f22])).
% 0.16/5.49 fof(f24,plain,(
% 0.16/5.49 ![X0]: (~class_LOrder_Ojoin__semilorder(X0)|class_Orderings_Oorder(X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f9])).
% 0.16/5.49 fof(f25,plain,(
% 0.16/5.49 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|class_OrderedGroup_Opordered__ab__group__add(X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f10])).
% 0.16/5.49 fof(f26,plain,(
% 0.16/5.49 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|class_LOrder_Ojoin__semilorder(X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f11])).
% 0.16/5.49 fof(f27,plain,(
% 0.16/5.49 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_OrderedGroup_Ocomm__monoid__add(X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f12])).
% 0.16/5.49 fof(f28,plain,(
% 0.16/5.49 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_OrderedGroup_Olordered__ab__group__abs(X0))),
% 0.16/5.49 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/5.49 fof(f29,plain,(
% 0.16/5.49 class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 0.16/5.49 inference(resolution,[status(thm)],[f28,f17])).
% 0.16/5.49 fof(f30,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~c_lessequals(c_plus(X0,X1,X2),X3,X2)|c_lessequals(X0,c_minus(X3,X1,X2),X2)|~class_OrderedGroup_Olordered__ab__group__abs(X2))),
% 0.16/5.49 inference(resolution,[status(thm)],[f21,f25])).
% 0.16/5.49 fof(f31,plain,(
% 0.16/5.49 class_OrderedGroup_Ocomm__monoid__add(t_b)),
% 0.16/5.49 inference(resolution,[status(thm)],[f27,f17])).
% 0.16/5.49 fof(f32,plain,(
% 0.16/5.49 ![X0]: (c_plus(c_0,X0,t_b)=X0)),
% 0.16/5.49 inference(resolution,[status(thm)],[f31,f19])).
% 0.16/5.49 fof(f33,plain,(
% 0.16/5.49 ![X0,X1]: (~class_OrderedGroup_Opordered__ab__group__add(t_b)|~c_lessequals(c_0,c_minus(X0,X1,t_b),t_b)|c_lessequals(X1,X0,t_b))),
% 0.16/5.49 inference(paramodulation,[status(thm)],[f32,f20])).
% 0.16/5.49 fof(f34,plain,(
% 0.16/5.49 ![X0,X1]: (~c_lessequals(c_0,c_minus(X0,X1,t_b),t_b)|c_lessequals(X1,X0,t_b)|~class_OrderedGroup_Olordered__ab__group__abs(t_b))),
% 0.16/5.49 inference(resolution,[status(thm)],[f33,f25])).
% 0.16/5.49 fof(f35,plain,(
% 0.16/5.49 ![X0,X1]: (~c_lessequals(c_0,c_minus(X0,X1,t_b),t_b)|c_lessequals(X1,X0,t_b))),
% 0.16/5.49 inference(forward_subsumption_resolution,[status(thm)],[f34,f29])).
% 0.16/5.49 fof(f36,plain,(
% 0.16/5.49 c_lessequals(v_k(v_x),v_f(v_x),t_b)),
% 0.16/5.49 inference(resolution,[status(thm)],[f35,f14])).
% 0.16/5.49 fof(f37,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~c_lessequals(X0,X1,X2)|~c_lessequals(X3,X0,X2)|c_lessequals(X3,X1,X2)|~class_LOrder_Ojoin__semilorder(X2))),
% 0.16/5.49 inference(resolution,[status(thm)],[f23,f24])).
% 0.16/5.49 fof(f38,plain,(
% 0.16/5.49 ![X0,X1,X2,X3]: (~c_lessequals(X0,X1,X2)|~c_lessequals(X3,X0,X2)|c_lessequals(X3,X1,X2)|~class_OrderedGroup_Olordered__ab__group__abs(X2))),
% 0.16/5.49 inference(resolution,[status(thm)],[f37,f26])).
% 0.16/5.49 fof(f39,plain,(
% 0.16/5.49 ![X0,X1,X2]: (~c_lessequals(X0,X1,t_b)|~c_lessequals(X2,X0,t_b)|c_lessequals(X2,X1,t_b))),
% 0.16/5.49 inference(resolution,[status(thm)],[f38,f29])).
% 0.16/5.49 fof(f40,plain,(
% 0.16/5.49 ![X0,X1,X2]: (~c_lessequals(c_plus(X0,X1,t_b),X2,t_b)|c_lessequals(X0,c_minus(X2,X1,t_b),t_b))),
% 0.16/5.49 inference(resolution,[status(thm)],[f30,f29])).
% 0.16/5.49 fof(f42,plain,(
% 0.16/5.49 ![X0,X1]: (~c_lessequals(X0,X1,t_b)|c_lessequals(c_0,c_minus(X1,X0,t_b),t_b))),
% 0.16/5.49 inference(paramodulation,[status(thm)],[f32,f40])).
% 0.16/5.49 fof(f46,plain,(
% 0.16/5.49 ~c_lessequals(v_g(v_x),v_f(v_x),t_b)),
% 0.16/5.49 inference(resolution,[status(thm)],[f42,f16])).
% 0.16/5.49 fof(f51,plain,(
% 0.16/5.49 ![X0]: (~c_lessequals(X0,v_f(v_x),t_b)|~c_lessequals(v_g(v_x),X0,t_b))),
% 0.16/5.49 inference(resolution,[status(thm)],[f46,f39])).
% 0.16/5.49 fof(f52,plain,(
% 0.16/5.49 ~c_lessequals(v_k(v_x),v_f(v_x),t_b)),
% 0.16/5.49 inference(resolution,[status(thm)],[f51,f15])).
% 0.16/5.49 fof(f54,plain,(
% 0.16/5.49 $false),
% 0.16/5.49 inference(forward_subsumption_resolution,[status(thm)],[f52,f36])).
% 0.16/5.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/5.54 % Elapsed time: 0.085975 seconds
% 0.20/5.54 % CPU time: 0.092573 seconds
% 0.20/5.54 % Total memory used: 2.834 MB
% 0.20/5.54 % Net memory used: 2.828 MB
%------------------------------------------------------------------------------