% SZS status Theorem for FOF_Finite.s % SZS output start Proof for FOF_Finite.s fof(f411,plain,( $false), inference(avatar_sat_refutation,[],[f129,f131,f133,f144,f146,f151,f234,f248,f299,f310,f331,f334,f340,f357,f378,f382,f406,f410])). fof(f410,plain,( spl3_3 | ~spl3_18 | ~spl3_21), inference(avatar_contradiction_clause,[],[f409])). fof(f409,plain,( $false | (spl3_3 | ~spl3_18 | ~spl3_21)), inference(subsumption_resolution,[],[f408,f53])). fof(f53,plain,( created_equal("john","john")), inference(cnf_transformation,[],[f1])). fof(f1,axiom,( created_equal("gotA","gotA") & created_equal("gotA","john") & ~created_equal("gotA","f") & ~created_equal("gotA","a") & created_equal("john","gotA") & created_equal("john","john") & ~created_equal("john","f") & ~created_equal("john","a") & ~created_equal("f","gotA") & ~created_equal("f","john") & ~created_equal("f","f") & ~created_equal("f","a") & ~created_equal("a","gotA") & ~created_equal("a","john") & ~created_equal("a","f") & ~created_equal("a","a") & human("gotA") & human("john") & ~human("f") & ~human("a") & "a" = grade_of("gotA") & "f" = grade_of("john") & "a" = grade_of("f") & "a" = grade_of("a") & "john" = john & "f" = f & "a" = a & ! [X0] : ("gotA" = X0 | "john" = X0 | "f" = X0 | "a" = X0)), file('FOF_Finite.s.p',equality_lost)). fof(f408,plain,( ~created_equal("john","john") | (spl3_3 | ~spl3_18 | ~spl3_21)), inference(forward_demodulation,[],[f368,f280])). fof(f280,plain,( "john" = sK1 | ~spl3_21), inference(avatar_component_clause,[],[f278])). fof(f278,plain,( spl3_21 <=> "john" = sK1), introduced(avatar_definition,[new_symbols(naming,[spl3_21])])). fof(f368,plain,( ~created_equal(sK1,"john") | (spl3_3 | ~spl3_18)), inference(backward_demodulation,[],[f97,f264])). fof(f264,plain,( "john" = sK2 | ~spl3_18), inference(avatar_component_clause,[],[f262])). fof(f262,plain,( spl3_18 <=> "john" = sK2), introduced(avatar_definition,[new_symbols(naming,[spl3_18])])). fof(f97,plain,( ~created_equal(sK1,sK2) | spl3_3), inference(avatar_component_clause,[],[f95])). fof(f95,plain,( spl3_3 <=> created_equal(sK1,sK2)), introduced(avatar_definition,[new_symbols(naming,[spl3_3])])). fof(f406,plain,( spl3_3 | ~spl3_16 | ~spl3_21), inference(avatar_contradiction_clause,[],[f405])). fof(f405,plain,( $false | (spl3_3 | ~spl3_16 | ~spl3_21)), inference(subsumption_resolution,[],[f404,f54])). fof(f54,plain,( created_equal("john","gotA")), inference(cnf_transformation,[],[f1])). fof(f404,plain,( ~created_equal("john","gotA") | (spl3_3 | ~spl3_16 | ~spl3_21)), inference(forward_demodulation,[],[f323,f280])). fof(f323,plain,( ~created_equal(sK1,"gotA") | (spl3_3 | ~spl3_16)), inference(backward_demodulation,[],[f97,f256])). fof(f256,plain,( "gotA" = sK2 | ~spl3_16), inference(avatar_component_clause,[],[f254])). fof(f254,plain,( spl3_16 <=> "gotA" = sK2), introduced(avatar_definition,[new_symbols(naming,[spl3_16])])). fof(f382,plain,( spl3_16 | spl3_18 | ~spl3_7 | spl3_17), inference(avatar_split_clause,[],[f381,f258,f112,f262,f254])). fof(f112,plain,( spl3_7 <=> human(sK2)), introduced(avatar_definition,[new_symbols(naming,[spl3_7])])). fof(f258,plain,( spl3_17 <=> "f" = sK2), introduced(avatar_definition,[new_symbols(naming,[spl3_17])])). fof(f381,plain,( "john" = sK2 | "gotA" = sK2 | (~spl3_7 | spl3_17)), inference(subsumption_resolution,[],[f380,f259])). fof(f259,plain,( "f" != sK2 | spl3_17), inference(avatar_component_clause,[],[f258])). fof(f380,plain,( "john" = sK2 | "f" = sK2 | "gotA" = sK2 | ~spl3_7), inference(subsumption_resolution,[],[f379,f39])). fof(f39,plain,( ~human("a")), inference(cnf_transformation,[],[f1])). fof(f379,plain,( human("a") | "john" = sK2 | "f" = sK2 | "gotA" = sK2 | ~spl3_7), inference(superposition,[],[f114,f31])). fof(f31,plain,( ( ! [X0] : ("a" = X0 | "john" = X0 | "f" = X0 | "gotA" = X0) )), inference(cnf_transformation,[],[f1])). fof(f114,plain,( human(sK2) | ~spl3_7), inference(avatar_component_clause,[],[f112])). fof(f378,plain,( spl3_3 | ~spl3_18 | ~spl3_19), inference(avatar_contradiction_clause,[],[f377])). fof(f377,plain,( $false | (spl3_3 | ~spl3_18 | ~spl3_19)), inference(subsumption_resolution,[],[f376,f57])). fof(f57,plain,( created_equal("gotA","john")), inference(cnf_transformation,[],[f1])). fof(f376,plain,( ~created_equal("gotA","john") | (spl3_3 | ~spl3_18 | ~spl3_19)), inference(forward_demodulation,[],[f368,f272])). fof(f272,plain,( "gotA" = sK1 | ~spl3_19), inference(avatar_component_clause,[],[f270])). fof(f270,plain,( spl3_19 <=> "gotA" = sK1), introduced(avatar_definition,[new_symbols(naming,[spl3_19])])). fof(f357,plain,( ~spl3_7 | ~spl3_17), inference(avatar_contradiction_clause,[],[f356])). fof(f356,plain,( $false | (~spl3_7 | ~spl3_17)), inference(subsumption_resolution,[],[f354,f40])). fof(f40,plain,( ~human("f")), inference(cnf_transformation,[],[f1])). fof(f354,plain,( human("f") | (~spl3_7 | ~spl3_17)), inference(backward_demodulation,[],[f114,f260])). fof(f260,plain,( "f" = sK2 | ~spl3_17), inference(avatar_component_clause,[],[f258])). fof(f340,plain,( ~spl3_8 | ~spl3_20), inference(avatar_contradiction_clause,[],[f339])). fof(f339,plain,( $false | (~spl3_8 | ~spl3_20)), inference(subsumption_resolution,[],[f337,f40])). fof(f337,plain,( human("f") | (~spl3_8 | ~spl3_20)), inference(backward_demodulation,[],[f120,f276])). fof(f276,plain,( "f" = sK1 | ~spl3_20), inference(avatar_component_clause,[],[f274])). fof(f274,plain,( spl3_20 <=> "f" = sK1), introduced(avatar_definition,[new_symbols(naming,[spl3_20])])). fof(f120,plain,( human(sK1) | ~spl3_8), inference(avatar_component_clause,[],[f118])). fof(f118,plain,( spl3_8 <=> human(sK1)), introduced(avatar_definition,[new_symbols(naming,[spl3_8])])). fof(f334,plain,( spl3_19 | spl3_20 | spl3_21 | ~spl3_8), inference(avatar_split_clause,[],[f333,f118,f278,f274,f270])). fof(f333,plain,( "john" = sK1 | "f" = sK1 | "gotA" = sK1 | ~spl3_8), inference(subsumption_resolution,[],[f332,f39])). fof(f332,plain,( human("a") | "john" = sK1 | "f" = sK1 | "gotA" = sK1 | ~spl3_8), inference(superposition,[],[f120,f31])). fof(f331,plain,( spl3_3 | ~spl3_16 | ~spl3_19), inference(avatar_contradiction_clause,[],[f330])). fof(f330,plain,( $false | (spl3_3 | ~spl3_16 | ~spl3_19)), inference(subsumption_resolution,[],[f329,f58])). fof(f58,plain,( created_equal("gotA","gotA")), inference(cnf_transformation,[],[f1])). fof(f329,plain,( ~created_equal("gotA","gotA") | (spl3_3 | ~spl3_16 | ~spl3_19)), inference(forward_demodulation,[],[f323,f272])). fof(f310,plain,( ~spl3_1 | ~spl3_5 | ~spl3_15), inference(avatar_contradiction_clause,[],[f309])). fof(f309,plain,( $false | (~spl3_1 | ~spl3_5 | ~spl3_15)), inference(subsumption_resolution,[],[f308,f40])). fof(f308,plain,( human("f") | (~spl3_1 | ~spl3_5 | ~spl3_15)), inference(forward_demodulation,[],[f305,f89])). fof(f89,plain,( "f" = grade_of("john") | ~spl3_1), inference(avatar_component_clause,[],[f88])). fof(f88,plain,( spl3_1 <=> "f" = grade_of("john")), introduced(avatar_definition,[new_symbols(naming,[spl3_1])])). fof(f305,plain,( human(grade_of("john")) | (~spl3_5 | ~spl3_15)), inference(backward_demodulation,[],[f104,f228])). fof(f228,plain,( "john" = sK0 | ~spl3_15), inference(avatar_component_clause,[],[f226])). fof(f226,plain,( spl3_15 <=> "john" = sK0), introduced(avatar_definition,[new_symbols(naming,[spl3_15])])). fof(f104,plain,( human(grade_of(sK0)) | ~spl3_5), inference(avatar_component_clause,[],[f102])). fof(f102,plain,( spl3_5 <=> human(grade_of(sK0))), introduced(avatar_definition,[new_symbols(naming,[spl3_5])])). fof(f299,plain,( spl3_13 | spl3_14 | spl3_15 | ~spl3_5), inference(avatar_split_clause,[],[f298,f102,f226,f222,f218])). fof(f218,plain,( spl3_13 <=> "gotA" = sK0), introduced(avatar_definition,[new_symbols(naming,[spl3_13])])). fof(f222,plain,( spl3_14 <=> "f" = sK0), introduced(avatar_definition,[new_symbols(naming,[spl3_14])])). fof(f298,plain,( "john" = sK0 | "f" = sK0 | "gotA" = sK0 | ~spl3_5), inference(subsumption_resolution,[],[f297,f39])). fof(f297,plain,( human("a") | "john" = sK0 | "f" = sK0 | "gotA" = sK0 | ~spl3_5), inference(forward_demodulation,[],[f295,f35])). fof(f35,plain,( "a" = grade_of("a")), inference(cnf_transformation,[],[f1])). fof(f295,plain,( human(grade_of("a")) | "john" = sK0 | "f" = sK0 | "gotA" = sK0 | ~spl3_5), inference(superposition,[],[f104,f31])). fof(f248,plain,( ~spl3_5 | ~spl3_14), inference(avatar_contradiction_clause,[],[f247])). fof(f247,plain,( $false | (~spl3_5 | ~spl3_14)), inference(subsumption_resolution,[],[f246,f39])). fof(f246,plain,( human("a") | (~spl3_5 | ~spl3_14)), inference(forward_demodulation,[],[f244,f36])). fof(f36,plain,( "a" = grade_of("f")), inference(cnf_transformation,[],[f1])). fof(f244,plain,( human(grade_of("f")) | (~spl3_5 | ~spl3_14)), inference(backward_demodulation,[],[f104,f224])). fof(f224,plain,( "f" = sK0 | ~spl3_14), inference(avatar_component_clause,[],[f222])). fof(f234,plain,( ~spl3_5 | ~spl3_13), inference(avatar_contradiction_clause,[],[f233])). fof(f233,plain,( $false | (~spl3_5 | ~spl3_13)), inference(subsumption_resolution,[],[f232,f39])). fof(f232,plain,( human("a") | (~spl3_5 | ~spl3_13)), inference(forward_demodulation,[],[f230,f38])). fof(f38,plain,( "a" = grade_of("gotA")), inference(cnf_transformation,[],[f1])). fof(f230,plain,( human(grade_of("gotA")) | (~spl3_5 | ~spl3_13)), inference(backward_demodulation,[],[f104,f220])). fof(f220,plain,( "gotA" = sK0 | ~spl3_13), inference(avatar_component_clause,[],[f218])). fof(f151,plain,( ~spl3_4), inference(avatar_contradiction_clause,[],[f150])). fof(f150,plain,( $false | ~spl3_4), inference(subsumption_resolution,[],[f38,f148])). fof(f148,plain,( "a" != grade_of("gotA") | ~spl3_4), inference(resolution,[],[f100,f42])). fof(f42,plain,( human("gotA")), inference(cnf_transformation,[],[f1])). fof(f100,plain,( ( ! [X3] : (~human(X3) | "a" != grade_of(X3)) ) | ~spl3_4), inference(avatar_component_clause,[],[f99])). fof(f99,plain,( spl3_4 <=> ! [X3] : ("a" != grade_of(X3) | ~human(X3))), introduced(avatar_definition,[new_symbols(naming,[spl3_4])])). fof(f146,plain,( spl3_6), inference(avatar_contradiction_clause,[],[f145])). fof(f145,plain,( $false | spl3_6), inference(subsumption_resolution,[],[f108,f41])). fof(f41,plain,( human("john")), inference(cnf_transformation,[],[f1])). fof(f108,plain,( ~human("john") | spl3_6), inference(avatar_component_clause,[],[f106])). fof(f106,plain,( spl3_6 <=> human("john")), introduced(avatar_definition,[new_symbols(naming,[spl3_6])])). fof(f144,plain,( spl3_1), inference(avatar_contradiction_clause,[],[f143])). fof(f143,plain,( $false | spl3_1), inference(subsumption_resolution,[],[f37,f90])). fof(f90,plain,( "f" != grade_of("john") | spl3_1), inference(avatar_component_clause,[],[f88])). fof(f37,plain,( "f" = grade_of("john")), inference(cnf_transformation,[],[f1])). fof(f133,plain,( spl3_5 | ~spl3_1 | spl3_8 | ~spl3_6 | spl3_4), inference(avatar_split_clause,[],[f132,f99,f106,f118,f88,f102])). fof(f132,plain,( ( ! [X3] : (~human(X3) | ~human("john") | human(sK1) | "f" != grade_of("john") | human(grade_of(sK0)) | "a" != grade_of(X3)) )), inference(global_subsumption,[],[f126])). fof(f126,plain,( ( ! [X3] : (~human("john") | "a" != grade_of(X3) | "f" != grade_of("john") | ~human(X3) | human(sK1) | human(grade_of(sK0))) )), inference(global_subsumption,[],[f18,f83])). fof(f83,plain,( ( ! [X3] : (human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK1)) )), inference(condensation,[],[f76])). fof(f76,plain,( ( ! [X3,X1] : (human(X1) | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK1)) )), inference(equality_resolution,[],[f64])). fof(f64,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK1)) )), inference(definition_unfolding,[],[f25,f32,f33,f32,f33,f34,f34])). fof(f34,plain,( "john" = john), inference(cnf_transformation,[],[f1])). fof(f33,plain,( "f" = f), inference(cnf_transformation,[],[f1])). fof(f32,plain,( "a" = a), inference(cnf_transformation,[],[f1])). fof(f25,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | a = f | a != grade_of(X3) | ~human(X3) | f != grade_of(john) | ~human(john) | human(sK1)) )), inference(cnf_transformation,[],[f12])). fof(f12,plain,( ! [X0,X1] : (((created_equal(X0,X1) & human(X1) & human(X0)) | X0 != X1) & (X0 = X1 | ~created_equal(X0,X1) | ~human(X1) | ~human(X0))) | human(grade_of(sK0)) | a = f | ! [X3] : (a != grade_of(X3) | ~human(X3)) | f != grade_of(john) | ~human(john) | (~created_equal(sK1,sK2) & human(sK2) & human(sK1))), inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10])). fof(f10,plain,( ? [X2] : human(grade_of(X2)) => human(grade_of(sK0))), introduced(choice_axiom,[])). fof(f11,plain,( ? [X4,X5] : (~created_equal(X4,X5) & human(X5) & human(X4)) => (~created_equal(sK1,sK2) & human(sK2) & human(sK1))), introduced(choice_axiom,[])). fof(f9,plain,( ! [X0,X1] : (((created_equal(X0,X1) & human(X1) & human(X0)) | X0 != X1) & (X0 = X1 | ~created_equal(X0,X1) | ~human(X1) | ~human(X0))) | ? [X2] : human(grade_of(X2)) | a = f | ! [X3] : (a != grade_of(X3) | ~human(X3)) | f != grade_of(john) | ~human(john) | ? [X4,X5] : (~created_equal(X4,X5) & human(X5) & human(X4))), inference(flattening,[],[f8])). fof(f8,plain,( ! [X0,X1] : (((created_equal(X0,X1) & human(X1) & human(X0)) | X0 != X1) & (X0 = X1 | (~created_equal(X0,X1) | ~human(X1) | ~human(X0)))) | ? [X2] : human(grade_of(X2)) | a = f | ! [X3] : (a != grade_of(X3) | ~human(X3)) | f != grade_of(john) | ~human(john) | ? [X4,X5] : (~created_equal(X4,X5) & human(X5) & human(X4))), inference(nnf_transformation,[],[f7])). fof(f7,plain,( ! [X0,X1] : ((created_equal(X0,X1) & human(X1) & human(X0)) <=> X0 = X1) | ? [X2] : human(grade_of(X2)) | a = f | ! [X3] : (a != grade_of(X3) | ~human(X3)) | f != grade_of(john) | ~human(john) | ? [X4,X5] : (~created_equal(X4,X5) & human(X5) & human(X4))), inference(flattening,[],[f6])). fof(f6,plain,( ! [X0,X1] : ((created_equal(X0,X1) & human(X1) & human(X0)) <=> X0 = X1) | ? [X2] : human(grade_of(X2)) | a = f | ! [X3] : (a != grade_of(X3) | ~human(X3)) | f != grade_of(john) | ~human(john) | ? [X4,X5] : (~created_equal(X4,X5) & (human(X5) & human(X4)))), inference(ennf_transformation,[],[f5])). fof(f5,plain,( ~(~! [X0,X1] : ((created_equal(X0,X1) & human(X1) & human(X0)) <=> X0 = X1) & ! [X2] : ~human(grade_of(X2)) & a != f & ? [X3] : (a = grade_of(X3) & human(X3)) & f = grade_of(john) & human(john) & ! [X4,X5] : ((human(X5) & human(X4)) => created_equal(X4,X5)))), inference(rectify,[],[f3])). fof(f3,negated_conjecture,( ~(~! [X1,X2] : ((created_equal(X1,X2) & human(X2) & human(X1)) <=> X1 = X2) & ! [X4] : ~human(grade_of(X4)) & a != f & ? [X3] : (a = grade_of(X3) & human(X3)) & f = grade_of(john) & human(john) & ! [X1,X2] : ((human(X2) & human(X1)) => created_equal(X1,X2)))), inference(negated_conjecture,[],[f2])). fof(f2,conjecture,( ~! [X1,X2] : ((created_equal(X1,X2) & human(X2) & human(X1)) <=> X1 = X2) & ! [X4] : ~human(grade_of(X4)) & a != f & ? [X3] : (a = grade_of(X3) & human(X3)) & f = grade_of(john) & human(john) & ! [X1,X2] : ((human(X2) & human(X1)) => created_equal(X1,X2))), file('FOF_Finite.s.p',prove_formulae)). fof(f18,plain,( "a" != "f"), inference(cnf_transformation,[],[f4])). fof(f4,plain,( "a" != "f" & "a" != "john" & "f" != "john" & "a" != "gotA" & "f" != "gotA" & "john" != "gotA"), introduced(distinctness_axiom,[])). fof(f131,plain,( ~spl3_6 | spl3_7 | spl3_5 | ~spl3_1 | spl3_4), inference(avatar_split_clause,[],[f130,f99,f88,f102,f112,f106])). fof(f130,plain,( ( ! [X3] : ("a" != grade_of(X3) | "f" != grade_of("john") | ~human(X3) | human(grade_of(sK0)) | human(sK2) | ~human("john")) )), inference(global_subsumption,[],[f124])). fof(f124,plain,( ( ! [X3] : (~human(X3) | ~human("john") | human(grade_of(sK0)) | "f" != grade_of("john") | "a" != grade_of(X3) | human(sK2)) )), inference(global_subsumption,[],[f18,f84])). fof(f84,plain,( ( ! [X3] : (human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK2)) )), inference(condensation,[],[f75])). fof(f75,plain,( ( ! [X3,X1] : (human(X1) | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK2)) )), inference(equality_resolution,[],[f63])). fof(f63,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | human(sK2)) )), inference(definition_unfolding,[],[f26,f32,f33,f32,f33,f34,f34])). fof(f26,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | a = f | a != grade_of(X3) | ~human(X3) | f != grade_of(john) | ~human(john) | human(sK2)) )), inference(cnf_transformation,[],[f12])). fof(f129,plain,( ~spl3_6 | ~spl3_1 | ~spl3_3 | spl3_5 | spl3_4), inference(avatar_split_clause,[],[f128,f99,f102,f95,f88,f106])). fof(f128,plain,( ( ! [X3] : ("a" != grade_of(X3) | human(grade_of(sK0)) | ~created_equal(sK1,sK2) | "f" != grade_of("john") | ~human("john") | ~human(X3)) )), inference(global_subsumption,[],[f122])). fof(f122,plain,( ( ! [X3] : ("a" != grade_of(X3) | ~created_equal(sK1,sK2) | ~human(X3) | human(grade_of(sK0)) | ~human("john") | "f" != grade_of("john")) )), inference(global_subsumption,[],[f18,f85])). fof(f85,plain,( ( ! [X3] : (human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | ~created_equal(sK1,sK2)) )), inference(condensation,[],[f74])). fof(f74,plain,( ( ! [X3,X1] : (human(X1) | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | ~created_equal(sK1,sK2)) )), inference(equality_resolution,[],[f62])). fof(f62,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | "a" = "f" | "a" != grade_of(X3) | ~human(X3) | "f" != grade_of("john") | ~human("john") | ~created_equal(sK1,sK2)) )), inference(definition_unfolding,[],[f27,f32,f33,f32,f33,f34,f34])). fof(f27,plain,( ( ! [X3,X0,X1] : (human(X1) | X0 != X1 | human(grade_of(sK0)) | a = f | a != grade_of(X3) | ~human(X3) | f != grade_of(john) | ~human(john) | ~created_equal(sK1,sK2)) )), inference(cnf_transformation,[],[f12])). % SZS output end Proof for FOF_Finite.s