%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 12:02:30 PM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n026.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 13:26:44 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/5.39 fof(f1,negated_conjecture,(
% 0.09/5.39 v_f(c_0) = c_0 ),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f2,negated_conjecture,(
% 0.09/5.39 c_less(c_0,v_c,t_a) ),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f3,negated_conjecture,(
% 0.09/5.39 v_x = c_0 ),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f4,negated_conjecture,(
% 0.09/5.39 ~ 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) ),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f5,negated_conjecture,(
% 0.09/5.39 class_Ring__and__Field_Oordered__idom(t_a) ),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f6,axiom,(
% 0.09/5.39 (![T_a]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)| c_HOL_Oabs(c_0,T_a) = c_0 ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f7,axiom,(
% 0.09/5.39 (![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) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f8,axiom,(
% 0.09/5.39 (![T_a,V_x,V_y]: (( ~ class_Orderings_Oorder(T_a)| ~ c_less(V_x,V_y,T_a)| c_lessequals(V_x,V_y,T_a) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f9,axiom,(
% 0.09/5.39 (![T_a,V_b,V_a]: (( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)| ~ c_lessequals(c_0,V_b,T_a)| ~ c_lessequals(c_0,V_a,T_a)| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f10,axiom,(
% 0.09/5.39 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f11,axiom,(
% 0.09/5.39 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_Orderings_Oorder(T) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f12,axiom,(
% 0.09/5.39 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_OrderedGroup_Olordered__ab__group__abs(T) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f13,plain,(
% 0.09/5.39 v_f(c_0)=c_0),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/5.39 fof(f14,plain,(
% 0.09/5.39 c_less(c_0,v_c,t_a)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/5.39 fof(f15,plain,(
% 0.09/5.39 v_x=c_0),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/5.39 fof(f16,plain,(
% 0.09/5.39 ~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)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.09/5.39 fof(f17,plain,(
% 0.09/5.39 class_Ring__and__Field_Oordered__idom(t_a)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/5.39 fof(f18,plain,(
% 0.09/5.39 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_HOL_Oabs(c_0,X0)=c_0)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/5.39 fof(f19,plain,(
% 0.09/5.39 ![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)))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f7])).
% 0.09/5.39 fof(f20,plain,(
% 0.09/5.39 ![X0,X1]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/5.39 fof(f21,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~class_Orderings_Oorder(X0)|~c_less(X1,X2,X0)|c_lessequals(X1,X2,X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/5.39 fof(f22,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~class_Ring__and__Field_Opordered__cancel__semiring(X0)|~c_lessequals(c_0,X1,X0)|~c_lessequals(c_0,X2,X0)|c_lessequals(c_0,c_times(X2,X1,X0),X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/5.39 fof(f23,plain,(
% 0.09/5.39 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_Ring__and__Field_Opordered__cancel__semiring(X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/5.39 fof(f24,plain,(
% 0.09/5.39 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_Orderings_Oorder(X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/5.39 fof(f25,plain,(
% 0.09/5.39 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_OrderedGroup_Olordered__ab__group__abs(X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/5.39 fof(f26,plain,(
% 0.09/5.39 v_f(v_x)=c_0),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f13])).
% 0.09/5.39 fof(f27,plain,(
% 0.09/5.39 v_f(v_x)=v_x),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f26])).
% 0.09/5.39 fof(f28,plain,(
% 0.09/5.39 c_less(v_x,v_c,t_a)),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f14])).
% 0.09/5.39 fof(f29,plain,(
% 0.09/5.39 ~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)),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f27,f16])).
% 0.09/5.39 fof(f30,plain,(
% 0.09/5.39 class_Ring__and__Field_Opordered__cancel__semiring(t_a)),
% 0.09/5.39 inference(resolution,[status(thm)],[f23,f17])).
% 0.09/5.39 fof(f31,plain,(
% 0.09/5.39 class_Orderings_Oorder(t_a)),
% 0.09/5.39 inference(resolution,[status(thm)],[f24,f17])).
% 0.09/5.39 fof(f32,plain,(
% 0.09/5.39 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_HOL_Oabs(v_x,X0)=c_0)),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f18])).
% 0.09/5.39 fof(f33,plain,(
% 0.09/5.39 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_HOL_Oabs(v_x,X0)=v_x)),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f32])).
% 0.09/5.39 fof(f34,plain,(
% 0.09/5.39 ![X0,X1]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0))),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f20])).
% 0.09/5.39 fof(f35,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~class_Ring__and__Field_Opordered__cancel__semiring(X0)|~c_lessequals(v_x,X1,X0)|~c_lessequals(c_0,X2,X0)|c_lessequals(c_0,c_times(X2,X1,X0),X0))),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f22])).
% 0.09/5.39 fof(f36,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~class_Ring__and__Field_Opordered__cancel__semiring(X0)|~c_lessequals(v_x,X1,X0)|~c_lessequals(v_x,X2,X0)|c_lessequals(c_0,c_times(X2,X1,X0),X0))),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f35])).
% 0.09/5.39 fof(f37,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~class_Ring__and__Field_Opordered__cancel__semiring(X0)|~c_lessequals(v_x,X1,X0)|~c_lessequals(v_x,X2,X0)|c_lessequals(v_x,c_times(X2,X1,X0),X0))),
% 0.09/5.39 inference(forward_demodulation,[status(thm)],[f15,f36])).
% 0.09/5.39 fof(f38,plain,(
% 0.09/5.39 ![X0,X1]: (~c_less(X0,X1,t_a)|c_lessequals(X0,X1,t_a))),
% 0.09/5.39 inference(resolution,[status(thm)],[f31,f21])).
% 0.09/5.39 fof(f39,plain,(
% 0.09/5.39 c_lessequals(v_x,v_c,t_a)),
% 0.09/5.39 inference(resolution,[status(thm)],[f38,f28])).
% 0.09/5.39 fof(f40,plain,(
% 0.09/5.39 class_OrderedGroup_Olordered__ab__group__abs(t_a)),
% 0.09/5.39 inference(resolution,[status(thm)],[f25,f17])).
% 0.09/5.39 fof(f41,plain,(
% 0.09/5.39 ![X0]: (c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a))),
% 0.09/5.39 inference(resolution,[status(thm)],[f40,f34])).
% 0.09/5.39 fof(f42,plain,(
% 0.09/5.39 c_HOL_Oabs(v_x,t_a)=v_x),
% 0.09/5.39 inference(resolution,[status(thm)],[f40,f33])).
% 0.09/5.39 fof(f43,plain,(
% 0.09/5.39 ~c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)),
% 0.09/5.39 inference(backward_demodulation,[status(thm)],[f42,f29])).
% 0.09/5.39 fof(f45,plain,(
% 0.09/5.39 ~class_Ring__and__Field_Opordered__cancel__semiring(t_a)|~c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)|~c_lessequals(v_x,v_c,t_a)),
% 0.09/5.39 inference(resolution,[status(thm)],[f43,f37])).
% 0.09/5.39 fof(f46,plain,(
% 0.09/5.39 ~c_lessequals(v_x,c_HOL_Oabs(v_h(v_x),t_a),t_a)|~c_lessequals(v_x,v_c,t_a)),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f45,f30])).
% 0.09/5.39 fof(f48,plain,(
% 0.09/5.39 ~c_lessequals(v_x,v_c,t_a)),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f46,f41])).
% 0.09/5.39 fof(f49,plain,(
% 0.09/5.39 $false),
% 0.09/5.39 inference(backward_subsumption_resolution,[status(thm)],[f39,f48])).
% 0.09/5.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.41 % Elapsed time: 0.047907 seconds
% 0.13/5.41 % CPU time: 0.145029 seconds
% 0.13/5.41 % Total memory used: 66.541 MB
% 0.13/5.41 % Net memory used: 66.046 MB
%------------------------------------------------------------------------------