%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ANA025-2 : 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 : n015.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 12:02:31 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 13:27:52 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.24/0.49 % Refutation found
% 0.24/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.49 fof(f1,axiom,(
% 0.24/0.49 (![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) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f2,axiom,(
% 0.24/0.49 (![T_a,V_y,V_x]: (( ~ class_Orderings_Olinorder(T_a)| c_less(V_y,V_x,T_a)| c_lessequals(V_x,V_y,T_a) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f3,axiom,(
% 0.24/0.49 (![T_b,V_y,V_z,V_x]: (( ~ class_Orderings_Olinorder(T_b)| ~ c_lessequals(V_y,V_z,T_b)| ~ c_lessequals(V_x,V_z,T_b)| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f4,axiom,(
% 0.24/0.49 (![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) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f5,axiom,(
% 0.24/0.49 (![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) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f6,negated_conjecture,(
% 0.24/0.49 ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f7,negated_conjecture,(
% 0.24/0.49 ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f8,axiom,(
% 0.24/0.49 (![T]: (( ~ class_LOrder_Ojoin__semilorder(T)| class_Orderings_Oorder(T) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f9,axiom,(
% 0.24/0.49 (![T]: (( ~ class_OrderedGroup_Olordered__ab__group__abs(T)| class_LOrder_Ojoin__semilorder(T) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f10,axiom,(
% 0.24/0.49 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_Orderings_Olinorder(T) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f11,axiom,(
% 0.24/0.49 (![T]: (( ~ class_Ring__and__Field_Oordered__idom(T)| class_OrderedGroup_Olordered__ab__group__abs(T) ) ))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f12,negated_conjecture,(
% 0.24/0.49 class_Ring__and__Field_Oordered__idom(t_b) ),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.49 fof(f13,plain,(
% 0.24/0.49 ![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)))),
% 0.24/0.49 inference(miniscoping,[status(thm)],[f1])).
% 0.24/0.49 fof(f14,plain,(
% 0.24/0.49 ![X0,X1]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f13])).
% 0.24/0.49 fof(f15,plain,(
% 0.24/0.49 ![X0,X1,X2]: (~class_Orderings_Olinorder(X0)|c_less(X1,X2,X0)|c_lessequals(X2,X1,X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f2])).
% 0.24/0.49 fof(f16,plain,(
% 0.24/0.49 ![X0,X1,X2,X3]: (~class_Orderings_Olinorder(X0)|~c_lessequals(X1,X2,X0)|~c_lessequals(X3,X2,X0)|c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f3])).
% 0.24/0.49 fof(f17,plain,(
% 0.24/0.49 ![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))),
% 0.24/0.49 inference(miniscoping,[status(thm)],[f4])).
% 0.24/0.49 fof(f18,plain,(
% 0.24/0.49 ![X0,X1,X2,X3]: (~class_Orderings_Oorder(X0)|~c_lessequals(X1,X2,X0)|~c_lessequals(X3,X1,X0)|c_lessequals(X3,X2,X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f17])).
% 0.24/0.49 fof(f19,plain,(
% 0.24/0.49 ![X0,X1,X2]: (~class_Orderings_Oorder(X0)|~c_less(X1,X2,X0)|c_lessequals(X1,X2,X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f5])).
% 0.24/0.49 fof(f20,plain,(
% 0.24/0.49 ~c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f6])).
% 0.24/0.49 fof(f21,plain,(
% 0.24/0.49 ~c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f7])).
% 0.24/0.49 fof(f22,plain,(
% 0.24/0.49 ![X0]: (~class_LOrder_Ojoin__semilorder(X0)|class_Orderings_Oorder(X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f8])).
% 0.24/0.49 fof(f23,plain,(
% 0.24/0.49 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|class_LOrder_Ojoin__semilorder(X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f9])).
% 0.24/0.49 fof(f24,plain,(
% 0.24/0.49 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_Orderings_Olinorder(X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f10])).
% 0.24/0.49 fof(f25,plain,(
% 0.24/0.49 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|class_OrderedGroup_Olordered__ab__group__abs(X0))),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f11])).
% 0.24/0.49 fof(f26,plain,(
% 0.24/0.49 class_Ring__and__Field_Oordered__idom(t_b)),
% 0.24/0.49 inference(cnf_transformation,[status(thm)],[f12])).
% 0.24/0.49 fof(f27,plain,(
% 0.24/0.49 class_Orderings_Olinorder(t_b)),
% 0.24/0.49 inference(resolution,[status(thm)],[f24,f26])).
% 0.24/0.49 fof(f28,plain,(
% 0.24/0.49 class_OrderedGroup_Olordered__ab__group__abs(t_b)),
% 0.24/0.49 inference(resolution,[status(thm)],[f25,f26])).
% 0.24/0.49 fof(f29,plain,(
% 0.24/0.49 ![X0]: (c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b))),
% 0.24/0.49 inference(resolution,[status(thm)],[f28,f14])).
% 0.24/0.49 fof(f30,plain,(
% 0.24/0.49 ![X0,X1,X2]: (~c_lessequals(X0,X1,t_b)|~c_lessequals(X2,X1,t_b)|c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b))),
% 0.24/0.49 inference(resolution,[status(thm)],[f16,f27])).
% 0.24/0.49 fof(f31,plain,(
% 0.24/0.49 ~c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)|~c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)),
% 0.24/0.49 inference(resolution,[status(thm)],[f30,f21])).
% 0.24/0.49 fof(f32,definition,(
% 0.24/0.49 sQ0_spl <=> (c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b))),
% 0.24/0.49 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.24/0.49 fof(f34,plain,(
% 0.24/0.49 ~c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)|sQ0_spl),
% 0.24/0.49 inference(component_clause,[status(thm)],[f32])).
% 0.24/0.49 fof(f35,definition,(
% 0.24/0.49 sQ1_spl <=> (c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b))),
% 0.24/0.49 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.24/0.49 fof(f37,plain,(
% 0.24/0.49 ~c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)|sQ1_spl),
% 0.24/0.49 inference(component_clause,[status(thm)],[f35])).
% 0.24/0.49 fof(f38,plain,(
% 0.24/0.49 ~sQ0_spl|~sQ1_spl),
% 0.24/0.49 inference(split_clause,[status(thm)],[f31,f32,f35])).
% 0.24/0.49 fof(f39,plain,(
% 0.24/0.49 $false|sQ0_spl),
% 0.24/0.49 inference(forward_subsumption_resolution,[status(thm)],[f34,f29])).
% 0.24/0.49 fof(f40,plain,(
% 0.24/0.49 sQ0_spl),
% 0.24/0.49 inference(contradiction_clause,[status(thm)],[f39])).
% 0.24/0.49 fof(f41,plain,(
% 0.24/0.49 ![X0]: (~class_OrderedGroup_Olordered__ab__group__abs(X0)|class_Orderings_Oorder(X0))),
% 0.24/0.49 inference(resolution,[status(thm)],[f23,f22])).
% 0.24/0.49 fof(f42,plain,(
% 0.24/0.49 ![X0,X1,X2]: (~c_less(X0,X1,X2)|c_lessequals(X0,X1,X2)|~class_OrderedGroup_Olordered__ab__group__abs(X2))),
% 0.24/0.49 inference(resolution,[status(thm)],[f19,f41])).
% 0.24/0.49 fof(f43,plain,(
% 0.24/0.49 ![X0,X1]: (~c_less(X0,X1,t_b)|c_lessequals(X0,X1,t_b))),
% 0.24/0.49 inference(resolution,[status(thm)],[f42,f28])).
% 0.24/0.49 fof(f44,plain,(
% 0.24/0.49 ![X0,X1]: (c_lessequals(X0,X1,t_b)|~class_Orderings_Olinorder(t_b)|c_lessequals(X1,X0,t_b))),
% 0.24/0.49 inference(resolution,[status(thm)],[f43,f15])).
% 0.24/0.49 fof(f45,definition,(
% 0.24/0.49 ![X0,X1]: (sQ2_spl <=> (c_lessequals(X0,X1,t_b)|c_lessequals(X1,X0,t_b)))),
% 0.24/0.49 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.24/0.49 fof(f46,plain,(
% 0.24/0.49 ![X0,X1]: (c_lessequals(X0,X1,t_b)|c_lessequals(X1,X0,t_b)|~sQ2_spl)),
% 0.24/0.49 inference(component_clause,[status(thm)],[f45])).
% 0.24/0.49 fof(f48,definition,(
% 0.24/0.49 sQ3_spl <=> (class_Orderings_Olinorder(t_b))),
% 0.24/0.49 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.24/0.49 fof(f50,plain,(
% 0.24/0.49 ~class_Orderings_Olinorder(t_b)|sQ3_spl),
% 0.24/0.49 inference(component_clause,[status(thm)],[f48])).
% 0.24/0.49 fof(f51,plain,(
% 0.24/0.49 sQ2_spl|~sQ3_spl),
% 0.24/0.49 inference(split_clause,[status(thm)],[f44,f45,f48])).
% 0.24/0.49 fof(f54,plain,(
% 0.24/0.49 c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)|~sQ2_spl),
% 0.24/0.49 inference(resolution,[status(thm)],[f46,f20])).
% 0.24/0.49 fof(f58,plain,(
% 0.24/0.49 ![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))),
% 0.24/0.49 inference(resolution,[status(thm)],[f18,f41])).
% 0.24/0.50 fof(f59,plain,(
% 0.24/0.50 ![X0,X1,X2]: (~c_lessequals(X0,X1,t_b)|~c_lessequals(X2,X0,t_b)|c_lessequals(X2,X1,t_b))),
% 0.24/0.50 inference(resolution,[status(thm)],[f58,f28])).
% 0.24/0.50 fof(f60,plain,(
% 0.24/0.50 ![X0]: (~c_lessequals(X0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)|~c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X0,t_b)|sQ1_spl)),
% 0.24/0.50 inference(resolution,[status(thm)],[f59,f37])).
% 0.24/0.50 fof(f68,plain,(
% 0.24/0.50 ~c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)|~sQ2_spl|sQ1_spl),
% 0.24/0.50 inference(resolution,[status(thm)],[f54,f60])).
% 0.24/0.50 fof(f69,plain,(
% 0.24/0.50 ~sQ0_spl|~sQ2_spl|sQ1_spl),
% 0.24/0.50 inference(split_clause,[status(thm)],[f68,f32,f45,f35])).
% 0.24/0.50 fof(f70,plain,(
% 0.24/0.50 $false|sQ3_spl),
% 0.24/0.50 inference(forward_subsumption_resolution,[status(thm)],[f50,f27])).
% 0.24/0.50 fof(f71,plain,(
% 0.24/0.50 sQ3_spl),
% 0.24/0.50 inference(contradiction_clause,[status(thm)],[f70])).
% 0.24/0.50 fof(f72,plain,(
% 0.24/0.50 $false),
% 0.24/0.50 inference(sat_refutation,[status(thm)],[f38,f40,f51,f69,f71])).
% 0.24/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.52 % Elapsed time: 0.060372 seconds
% 0.24/0.52 % CPU time: 0.149276 seconds
% 0.24/0.52 % Total memory used: 17.017 MB
% 0.24/0.52 % Net memory used: 16.620 MB
%------------------------------------------------------------------------------