%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA019-2 : 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 : n004.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 0.14s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n004.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 13:24:05 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.43 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.47 fof(f1,negated_conjecture,(
% 0.14/0.47 v_f(c_0) = c_0 ),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f2,negated_conjecture,(
% 0.14/0.47 c_less(c_0,v_x,t_a) ),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f3,negated_conjecture,(
% 0.14/0.47 (![V_U]: (c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f4,negated_conjecture,(
% 0.14/0.47 (![V_U]: (( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a)| ~ c_less(c_0,V_U,t_a) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f5,negated_conjecture,(
% 0.14/0.47 class_Ring__and__Field_Oordered__idom(t_a) ),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f6,axiom,(
% 0.14/0.47 (![V_x]: (( ~ c_less(c_0,V_x,tc_nat)| V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f7,axiom,(
% 0.14/0.47 (![V_n]: (( c_less(c_0,V_n,tc_nat)| V_n = c_0 ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f8,axiom,(
% 0.14/0.47 (![T_a]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)| c_HOL_Oabs(c_0,T_a) = c_0 ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f9,axiom,(
% 0.14/0.47 (![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) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f10,axiom,(
% 0.14/0.47 (![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) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f11,axiom,(
% 0.14/0.47 (![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) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f12,axiom,(
% 0.14/0.47 (![T]: (( ~ class_LOrder_Ojoin__semilorder(T)| class_Orderings_Oorder(T) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f13,axiom,(
% 0.14/0.47 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_LOrder_Ojoin__semilorder(T) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f14,axiom,(
% 0.14/0.47 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f15,axiom,(
% 0.14/0.47 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_OrderedGroup_Olordered__ab__group__abs(T) ) ))),
% 0.14/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f16,plain,(
% 0.14/0.47 v_f(c_0)=c_0),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.47 fof(f17,plain,(
% 0.14/0.47 c_less(c_0,v_x,t_a)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.47 fof(f18,plain,(
% 0.14/0.47 ![X0]: (c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.47 fof(f19,plain,(
% 0.14/0.47 ![X0]: (~c_lessequals(c_HOL_Oabs(v_f(v_xa(X0)),t_a),c_times(X0,c_HOL_Oabs(v_h(v_xa(X0)),t_a),t_a),t_a)|~c_less(c_0,X0,t_a))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.47 fof(f20,plain,(
% 0.14/0.47 class_Ring__and__Field_Oordered__idom(t_a)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.47 fof(f21,plain,(
% 0.14/0.47 ![X0]: (~c_less(c_0,X0,tc_nat)|X0=c_Suc(c_minus(X0,c_1,tc_nat)))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.47 fof(f22,plain,(
% 0.14/0.47 ![X0]: (c_less(c_0,X0,tc_nat)|X0=c_0)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/0.47 fof(f23,plain,(
% 0.14/0.47 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_HOL_Oabs(c_0,X0)=c_0)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.47 fof(f24,plain,(
% 0.14/0.47 ![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)))),
% 0.14/0.47 inference(miniscoping,[status(thm)],[f9])).
% 0.14/0.47 fof(f25,plain,(
% 0.14/0.47 ![X0,X1]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f24])).
% 0.14/0.47 fof(f26,plain,(
% 0.14/0.47 ![X0,X1,X2]: (~class_Orderings_Oorder(X0)|~c_less(X1,X2,X0)|c_lessequals(X1,X2,X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.47 fof(f27,plain,(
% 0.14/0.47 ![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))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.47 fof(f28,plain,(
% 0.14/0.47 ![X0]: (~class_LOrder_Ojoin__semilorder(X0)|class_Orderings_Oorder(X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.47 fof(f29,plain,(
% 0.14/0.47 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_LOrder_Ojoin__semilorder(X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.47 fof(f30,plain,(
% 0.14/0.47 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_Ring__and__Field_Opordered__cancel__semiring(X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/0.47 fof(f31,plain,(
% 0.14/0.47 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_OrderedGroup_Olordered__ab__group__abs(X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/0.47 fof(f32,plain,(
% 0.14/0.47 class_LOrder_Ojoin__semilorder(t_a)),
% 0.14/0.47 inference(resolution,[status(thm)],[f29,f20])).
% 0.14/0.47 fof(f33,plain,(
% 0.14/0.47 class_Orderings_Oorder(t_a)),
% 0.14/0.47 inference(resolution,[status(thm)],[f32,f28])).
% 0.14/0.47 fof(f34,plain,(
% 0.14/0.47 class_Ring__and__Field_Opordered__cancel__semiring(t_a)),
% 0.14/0.47 inference(resolution,[status(thm)],[f30,f20])).
% 0.14/0.47 fof(f35,plain,(
% 0.14/0.47 class_OrderedGroup_Olordered__ab__group__abs(t_a)),
% 0.14/0.47 inference(resolution,[status(thm)],[f31,f20])).
% 0.14/0.47 fof(f36,plain,(
% 0.14/0.47 ![X0]: (X0=c_0|X0=c_Suc(c_minus(X0,c_1,tc_nat)))),
% 0.14/0.47 inference(resolution,[status(thm)],[f22,f21])).
% 0.14/0.47 fof(f37,plain,(
% 0.14/0.47 c_HOL_Oabs(c_0,t_a)=c_0),
% 0.14/0.47 inference(resolution,[status(thm)],[f23,f35])).
% 0.14/0.47 fof(f38,plain,(
% 0.14/0.47 ![X0]: (c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a))),
% 0.14/0.47 inference(resolution,[status(thm)],[f25,f35])).
% 0.14/0.47 fof(f40,plain,(
% 0.14/0.47 ~class_Orderings_Oorder(t_a)|c_lessequals(c_0,v_x,t_a)),
% 0.14/0.47 inference(resolution,[status(thm)],[f26,f17])).
% 0.14/0.47 fof(f42,definition,(
% 0.14/0.47 sQ0_spl <=> (class_Orderings_Oorder(t_a))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f44,plain,(
% 0.14/0.47 ~class_Orderings_Oorder(t_a)|sQ0_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f42])).
% 0.14/0.47 fof(f45,definition,(
% 0.14/0.47 sQ1_spl <=> (c_lessequals(c_0,v_x,t_a))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f46,plain,(
% 0.14/0.47 c_lessequals(c_0,v_x,t_a)|~sQ1_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f45])).
% 0.14/0.47 fof(f48,plain,(
% 0.14/0.47 ~sQ0_spl|sQ1_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f40,f42,f45])).
% 0.14/0.47 fof(f56,plain,(
% 0.14/0.47 $false|sQ0_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f44,f33])).
% 0.14/0.47 fof(f57,plain,(
% 0.14/0.47 sQ0_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f56])).
% 0.14/0.47 fof(f58,plain,(
% 0.14/0.47 ![X0]: (c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X0,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)|X0=c_0)),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f36,f18])).
% 0.14/0.47 fof(f62,plain,(
% 0.14/0.47 ![X0,X1]: (~class_Ring__and__Field_Opordered__cancel__semiring(t_a)|~c_lessequals(c_0,X0,t_a)|c_lessequals(c_0,c_times(X0,c_HOL_Oabs(X1,t_a),t_a),t_a))),
% 0.14/0.47 inference(resolution,[status(thm)],[f27,f38])).
% 0.14/0.47 fof(f63,definition,(
% 0.14/0.47 sQ4_spl <=> (class_Ring__and__Field_Opordered__cancel__semiring(t_a))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f65,plain,(
% 0.14/0.47 ~class_Ring__and__Field_Opordered__cancel__semiring(t_a)|sQ4_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f63])).
% 0.14/0.47 fof(f74,definition,(
% 0.14/0.47 ![X0,X1]: (sQ7_spl <=> (~c_lessequals(c_0,X0,t_a)|c_lessequals(c_0,c_times(X0,c_HOL_Oabs(X1,t_a),t_a),t_a)))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f75,plain,(
% 0.14/0.47 ![X0,X1]: (~c_lessequals(c_0,X0,t_a)|c_lessequals(c_0,c_times(X0,c_HOL_Oabs(X1,t_a),t_a),t_a)|~sQ7_spl)),
% 0.14/0.47 inference(component_clause,[status(thm)],[f74])).
% 0.14/0.47 fof(f77,plain,(
% 0.14/0.47 ~sQ4_spl|sQ7_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f62,f63,f74])).
% 0.14/0.49 fof(f78,plain,(
% 0.14/0.49 $false|sQ4_spl),
% 0.14/0.49 inference(forward_subsumption_resolution,[status(thm)],[f65,f34])).
% 0.14/0.49 fof(f79,plain,(
% 0.14/0.49 sQ4_spl),
% 0.14/0.49 inference(contradiction_clause,[status(thm)],[f78])).
% 0.14/0.49 fof(f130,plain,(
% 0.14/0.49 ![X0]: (c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)|X0=c_0|X0=c_0)),
% 0.14/0.49 inference(paramodulation,[status(thm)],[f36,f58])).
% 0.14/0.49 fof(f131,plain,(
% 0.14/0.49 ![X0]: (c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)|X0=c_0)),
% 0.14/0.49 inference(duplicate_literals_removal,[status(thm)],[f130])).
% 0.14/0.49 fof(f149,plain,(
% 0.14/0.49 ![X0]: (c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(X0,t_a),t_a),t_a)|~sQ7_spl|~sQ1_spl)),
% 0.14/0.49 inference(resolution,[status(thm)],[f75,f46])).
% 0.14/0.49 fof(f194,plain,(
% 0.14/0.49 v_xa(v_x)=c_0|~c_less(c_0,v_x,t_a)),
% 0.14/0.49 inference(resolution,[status(thm)],[f131,f19])).
% 0.14/0.49 fof(f196,definition,(
% 0.14/0.49 sQ21_spl <=> (v_xa(v_x)=c_0)),
% 0.14/0.49 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.14/0.49 fof(f197,plain,(
% 0.14/0.49 v_xa(v_x)=c_0|~sQ21_spl),
% 0.14/0.49 inference(component_clause,[status(thm)],[f196])).
% 0.14/0.49 fof(f199,definition,(
% 0.14/0.49 sQ22_spl <=> (c_less(c_0,v_x,t_a))),
% 0.14/0.49 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.14/0.49 fof(f201,plain,(
% 0.14/0.49 ~c_less(c_0,v_x,t_a)|sQ22_spl),
% 0.14/0.49 inference(component_clause,[status(thm)],[f199])).
% 0.14/0.49 fof(f202,plain,(
% 0.14/0.49 sQ21_spl|~sQ22_spl),
% 0.14/0.49 inference(split_clause,[status(thm)],[f194,f196,f199])).
% 0.14/0.49 fof(f208,plain,(
% 0.14/0.49 ~c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a)|~c_less(c_0,v_x,t_a)|~sQ21_spl),
% 0.14/0.49 inference(paramodulation,[status(thm)],[f197,f19])).
% 0.14/0.49 fof(f213,definition,(
% 0.14/0.49 sQ25_spl <=> (c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a))),
% 0.14/0.49 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.14/0.49 fof(f215,plain,(
% 0.14/0.49 ~c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a)|sQ25_spl),
% 0.14/0.49 inference(component_clause,[status(thm)],[f213])).
% 0.14/0.49 fof(f216,plain,(
% 0.14/0.49 ~sQ25_spl|~sQ22_spl|~sQ21_spl),
% 0.14/0.49 inference(split_clause,[status(thm)],[f208,f213,f199,f196])).
% 0.14/0.49 fof(f217,plain,(
% 0.14/0.49 $false|sQ22_spl),
% 0.14/0.49 inference(forward_subsumption_resolution,[status(thm)],[f201,f17])).
% 0.14/0.49 fof(f218,plain,(
% 0.14/0.49 sQ22_spl),
% 0.14/0.49 inference(contradiction_clause,[status(thm)],[f217])).
% 0.14/0.49 fof(f219,plain,(
% 0.14/0.49 ~c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a)|sQ25_spl),
% 0.14/0.49 inference(forward_demodulation,[status(thm)],[f16,f215])).
% 0.14/0.49 fof(f220,plain,(
% 0.14/0.49 ~c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a)|sQ25_spl),
% 0.14/0.49 inference(forward_demodulation,[status(thm)],[f37,f219])).
% 0.14/0.49 fof(f221,plain,(
% 0.14/0.49 $false|~sQ7_spl|~sQ1_spl|sQ25_spl),
% 0.14/0.49 inference(forward_subsumption_resolution,[status(thm)],[f220,f149])).
% 0.14/0.49 fof(f222,plain,(
% 0.14/0.49 ~sQ7_spl|~sQ1_spl|sQ25_spl),
% 0.14/0.49 inference(contradiction_clause,[status(thm)],[f221])).
% 0.14/0.49 fof(f223,plain,(
% 0.14/0.49 $false),
% 0.14/0.49 inference(sat_refutation,[status(thm)],[f48,f57,f77,f79,f202,f216,f218,f222])).
% 0.14/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.51 % Elapsed time: 0.085980 seconds
% 0.14/0.51 % CPU time: 0.096401 seconds
% 0.14/0.51 % Total memory used: 3.340 MB
% 0.14/0.51 % Net memory used: 3.339 MB
%------------------------------------------------------------------------------