%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA015-2 : 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 : n011.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 12:02:30 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.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 : Mon Sep 21 13:23:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.38 fof(f1,axiom,(
% 0.08/0.38 (![T_a,V_a]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ))),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f2,axiom,(
% 0.08/0.38 (![T_a,V_a,V_b,V_c]: (( ~ class_OrderedGroup_Osemigroup__mult(T_a)| 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) ) ))),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f3,axiom,(
% 0.08/0.38 (![T_a,V_a,V_b]: (( ~ class_Ring__and__Field_Oordered__idom(T_a)| 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) ) ))),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f4,axiom,(
% 0.08/0.38 (![T_a,V_a,V_b,V_c]: (( ~ class_Ring__and__Field_Opordered__semiring(T_a)| ~ c_lessequals(V_a,V_b,T_a)| ~ c_lessequals(c_0,V_c,T_a)| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f5,negated_conjecture,(
% 0.08/0.39 (![V_U]: (c_lessequals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f6,negated_conjecture,(
% 0.08/0.39 (![V_U]: (~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f7,axiom,(
% 0.08/0.39 (![T]: (( ~ class_Ring__and__Field_Ofield(T)| class_OrderedGroup_Osemigroup__mult(T) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f8,axiom,(
% 0.08/0.39 (![T]: (( ~ class_Ring__and__Field_Oordered__field(T)| class_Ring__and__Field_Ofield(T) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f9,axiom,(
% 0.08/0.39 (![T]: (( ~ class_Ring__and__Field_Oordered__field(T)| class_Ring__and__Field_Oordered__idom(T) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f10,axiom,(
% 0.08/0.39 (![T]: (( ~ class_Ring__and__Field_Oordered__field(T)| class_Ring__and__Field_Opordered__semiring(T) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f11,axiom,(
% 0.08/0.39 (![T]: (( ~ class_Ring__and__Field_Oordered__field(T)| class_OrderedGroup_Olordered__ab__group__abs(T) ) ))),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f12,negated_conjecture,(
% 0.08/0.39 class_Ring__and__Field_Oordered__field(t_a) ),
% 0.08/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f13,plain,(
% 0.08/0.39 ![T_a]: (~class_OrderedGroup_Olordered__ab__group__abs(T_a)|(![V_a]: c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f1])).
% 0.08/0.39 fof(f14,plain,(
% 0.08/0.39 ![X0,X1]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.08/0.39 fof(f15,plain,(
% 0.08/0.39 ![T_a]: (~class_OrderedGroup_Osemigroup__mult(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)))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f2])).
% 0.08/0.39 fof(f16,plain,(
% 0.08/0.39 ![X0,X1,X2,X3]: (~class_OrderedGroup_Osemigroup__mult(X0)|c_times(c_times(X1,X2,X0),X3,X0)=c_times(X1,c_times(X2,X3,X0),X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f15])).
% 0.08/0.39 fof(f17,plain,(
% 0.08/0.39 ![T_a]: (~class_Ring__and__Field_Oordered__idom(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)))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f3])).
% 0.08/0.39 fof(f18,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~class_Ring__and__Field_Oordered__idom(X0)|c_HOL_Oabs(c_times(X1,X2,X0),X0)=c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.08/0.39 fof(f19,plain,(
% 0.08/0.39 ![X0,X1,X2,X3]: (~class_Ring__and__Field_Opordered__semiring(X0)|~c_lessequals(X1,X2,X0)|~c_lessequals(c_0,X3,X0)|c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.39 fof(f20,plain,(
% 0.08/0.39 ![X0]: (c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.39 fof(f21,plain,(
% 0.08/0.39 ![X0]: (~c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.39 fof(f22,plain,(
% 0.08/0.39 ![X0]: (~class_Ring__and__Field_Ofield(X0)|class_OrderedGroup_Osemigroup__mult(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.39 fof(f23,plain,(
% 0.08/0.39 ![X0]: (~class_Ring__and__Field_Oordered__field(X0)|class_Ring__and__Field_Ofield(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.08/0.39 fof(f24,plain,(
% 0.08/0.39 ![X0]: (~class_Ring__and__Field_Oordered__field(X0)|class_Ring__and__Field_Oordered__idom(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.39 fof(f25,plain,(
% 0.08/0.39 ![X0]: (~class_Ring__and__Field_Oordered__field(X0)|class_Ring__and__Field_Opordered__semiring(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.08/0.39 fof(f26,plain,(
% 0.08/0.39 ![X0]: (~class_Ring__and__Field_Oordered__field(X0)|class_OrderedGroup_Olordered__ab__group__abs(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.08/0.39 fof(f27,plain,(
% 0.08/0.39 class_Ring__and__Field_Oordered__field(t_a)),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.08/0.39 fof(f28,plain,(
% 0.08/0.39 class_Ring__and__Field_Ofield(t_a)),
% 0.08/0.39 inference(resolution,[status(thm)],[f23,f27])).
% 0.08/0.39 fof(f29,plain,(
% 0.08/0.39 class_OrderedGroup_Osemigroup__mult(t_a)),
% 0.08/0.39 inference(resolution,[status(thm)],[f28,f22])).
% 0.08/0.39 fof(f30,plain,(
% 0.08/0.39 class_Ring__and__Field_Oordered__idom(t_a)),
% 0.08/0.39 inference(resolution,[status(thm)],[f24,f27])).
% 0.08/0.39 fof(f31,plain,(
% 0.08/0.39 class_Ring__and__Field_Opordered__semiring(t_a)),
% 0.08/0.39 inference(resolution,[status(thm)],[f25,f27])).
% 0.08/0.39 fof(f32,plain,(
% 0.08/0.39 class_OrderedGroup_Olordered__ab__group__abs(t_a)),
% 0.08/0.39 inference(resolution,[status(thm)],[f26,f27])).
% 0.08/0.39 fof(f33,plain,(
% 0.08/0.39 ![X0]: (c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f14,f32])).
% 0.08/0.39 fof(f34,plain,(
% 0.08/0.39 ![X0,X1,X2]: (c_times(c_times(X0,X1,t_a),X2,t_a)=c_times(X0,c_times(X1,X2,t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f16,f29])).
% 0.08/0.39 fof(f36,plain,(
% 0.08/0.39 ![X0,X1]: (~c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(X0,X1,t_a))),t_a),t_a),c_times(X0,c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(X0,X1,t_a))),t_a),t_a),t_a),t_a))),
% 0.08/0.39 inference(paramodulation,[status(thm)],[f34,f21])).
% 0.08/0.39 fof(f49,plain,(
% 0.08/0.39 ![X0,X1]: (c_HOL_Oabs(c_times(X0,X1,t_a),t_a)=c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f18,f30])).
% 0.08/0.39 fof(f61,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~c_lessequals(X0,X1,t_a)|~c_lessequals(c_0,X2,t_a)|c_lessequals(c_times(X2,X0,t_a),c_times(X2,X1,t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f19,f31])).
% 0.08/0.39 fof(f63,plain,(
% 0.08/0.39 ![X0,X1]: (~c_lessequals(c_0,X0,t_a)|c_lessequals(c_times(X0,c_HOL_Oabs(v_g(X1),t_a),t_a),c_times(X0,c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f61,f20])).
% 0.08/0.39 fof(f119,plain,(
% 0.08/0.39 ![X0,X1]: (c_lessequals(c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(v_g(X1),t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),t_a))),
% 0.08/0.39 inference(resolution,[status(thm)],[f63,f33])).
% 0.08/0.39 fof(f120,plain,(
% 0.08/0.39 ![X0,X1]: (c_lessequals(c_HOL_Oabs(c_times(X0,v_g(X1),t_a),t_a),c_times(c_HOL_Oabs(X0,t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),t_a))),
% 0.08/0.39 inference(forward_demodulation,[status(thm)],[f49,f119])).
% 0.08/0.39 fof(f121,plain,(
% 0.08/0.39 $false),
% 0.08/0.39 inference(resolution,[status(thm)],[f120,f36])).
% 0.08/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.41 % Elapsed time: 0.045065 seconds
% 0.08/0.41 % CPU time: 0.126180 seconds
% 0.08/0.41 % Total memory used: 35.838 MB
% 0.08/0.41 % Net memory used: 35.549 MB
%------------------------------------------------------------------------------