TSTP Solution File: SET628+3 by PyRes---1.3
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- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:39:12 EDT 2022
% Result : Theorem 0.55s 0.74s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 02:30:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.74 # Version: 1.3
% 0.55/0.74 # SZS status Theorem
% 0.55/0.74 # SZS output start CNFRefutation
% 0.55/0.74 fof(not_equal_defn,axiom,(![B]:(![C]:(not_equal(B,C)<=>B!=C))),input).
% 0.55/0.74 fof(c21,axiom,(![B]:(![C]:((~not_equal(B,C)|B!=C)&(B=C|not_equal(B,C))))),inference(fof_nnf,status(thm),[not_equal_defn])).
% 0.55/0.74 fof(c22,axiom,((![B]:(![C]:(~not_equal(B,C)|B!=C)))&(![B]:(![C]:(B=C|not_equal(B,C))))),inference(shift_quantors,status(thm),[c21])).
% 0.55/0.74 fof(c24,axiom,(![X9]:(![X10]:(![X11]:(![X12]:((~not_equal(X9,X10)|X9!=X10)&(X11=X12|not_equal(X11,X12))))))),inference(shift_quantors,status(thm),[fof(c23,axiom,((![X9]:(![X10]:(~not_equal(X9,X10)|X9!=X10)))&(![X11]:(![X12]:(X11=X12|not_equal(X11,X12))))),inference(variable_rename,status(thm),[c22])).])).
% 0.55/0.74 cnf(c25,axiom,~not_equal(X39,X40)|X39!=X40,inference(split_conjunct,status(thm),[c24])).
% 0.55/0.74 cnf(symmetry,axiom,X31!=X32|X32=X31,eq_axiom).
% 0.55/0.74 cnf(c26,axiom,X43=X42|not_equal(X43,X42),inference(split_conjunct,status(thm),[c24])).
% 0.55/0.74 cnf(c52,plain,not_equal(X51,X52)|X52=X51,inference(resolution,status(thm),[c26, symmetry])).
% 0.55/0.74 cnf(c58,plain,not_equal(X63,X62)|~not_equal(X62,X63),inference(resolution,status(thm),[c52, c25])).
% 0.55/0.74 fof(empty_set_defn,axiom,(![B]:(~member(B,empty_set))),input).
% 0.55/0.74 fof(c37,axiom,(![B]:~member(B,empty_set)),inference(fof_simplification,status(thm),[empty_set_defn])).
% 0.55/0.74 fof(c38,axiom,(![X20]:~member(X20,empty_set)),inference(variable_rename,status(thm),[c37])).
% 0.55/0.74 cnf(c39,axiom,~member(X28,empty_set),inference(split_conjunct,status(thm),[c38])).
% 0.55/0.74 fof(empty_defn,axiom,(![B]:(empty(B)<=>(![C]:(~member(C,B))))),input).
% 0.55/0.74 fof(c10,axiom,(![B]:(empty(B)<=>(![C]:~member(C,B)))),inference(fof_simplification,status(thm),[empty_defn])).
% 0.55/0.74 fof(c11,axiom,(![B]:((~empty(B)|(![C]:~member(C,B)))&((?[C]:member(C,B))|empty(B)))),inference(fof_nnf,status(thm),[c10])).
% 0.55/0.74 fof(c12,axiom,((![B]:(~empty(B)|(![C]:~member(C,B))))&(![B]:((?[C]:member(C,B))|empty(B)))),inference(shift_quantors,status(thm),[c11])).
% 0.55/0.74 fof(c13,axiom,((![X3]:(~empty(X3)|(![X4]:~member(X4,X3))))&(![X5]:((?[X6]:member(X6,X5))|empty(X5)))),inference(variable_rename,status(thm),[c12])).
% 0.55/0.74 fof(c15,axiom,(![X3]:(![X4]:(![X5]:((~empty(X3)|~member(X4,X3))&(member(skolem0002(X5),X5)|empty(X5)))))),inference(shift_quantors,status(thm),[fof(c14,axiom,((![X3]:(~empty(X3)|(![X4]:~member(X4,X3))))&(![X5]:(member(skolem0002(X5),X5)|empty(X5)))),inference(skolemize,status(esa),[c13])).])).
% 0.55/0.74 cnf(c17,axiom,member(skolem0002(X68),X68)|empty(X68),inference(split_conjunct,status(thm),[c15])).
% 0.55/0.74 cnf(c64,plain,empty(empty_set),inference(resolution,status(thm),[c17, c39])).
% 0.55/0.74 cnf(c3,plain,X74!=X75|~empty(X74)|empty(X75),eq_axiom).
% 0.55/0.74 cnf(c68,plain,~empty(X77)|empty(X78)|not_equal(X78,X77),inference(resolution,status(thm),[c3, c52])).
% 0.55/0.74 cnf(c70,plain,empty(X79)|not_equal(X79,empty_set),inference(resolution,status(thm),[c68, c64])).
% 0.55/0.74 cnf(c16,axiom,~empty(X29)|~member(X30,X29),inference(split_conjunct,status(thm),[c15])).
% 0.55/0.74 fof(prove_th110,conjecture,(![B]:(intersect(B,B)<=>not_equal(B,empty_set))),input).
% 0.55/0.74 fof(c4,negated_conjecture,(~(![B]:(intersect(B,B)<=>not_equal(B,empty_set)))),inference(assume_negation,status(cth),[prove_th110])).
% 0.55/0.74 fof(c5,negated_conjecture,(?[B]:((~intersect(B,B)|~not_equal(B,empty_set))&(intersect(B,B)|not_equal(B,empty_set)))),inference(fof_nnf,status(thm),[c4])).
% 0.55/0.74 fof(c6,negated_conjecture,(?[X2]:((~intersect(X2,X2)|~not_equal(X2,empty_set))&(intersect(X2,X2)|not_equal(X2,empty_set)))),inference(variable_rename,status(thm),[c5])).
% 0.55/0.74 fof(c7,negated_conjecture,((~intersect(skolem0001,skolem0001)|~not_equal(skolem0001,empty_set))&(intersect(skolem0001,skolem0001)|not_equal(skolem0001,empty_set))),inference(skolemize,status(esa),[c6])).
% 0.55/0.74 cnf(c9,negated_conjecture,intersect(skolem0001,skolem0001)|not_equal(skolem0001,empty_set),inference(split_conjunct,status(thm),[c7])).
% 0.55/0.74 fof(intersect_defn,axiom,(![B]:(![C]:(intersect(B,C)<=>(?[D]:(member(D,B)&member(D,C)))))),input).
% 0.55/0.74 fof(c40,axiom,(![B]:(![C]:((~intersect(B,C)|(?[D]:(member(D,B)&member(D,C))))&((![D]:(~member(D,B)|~member(D,C)))|intersect(B,C))))),inference(fof_nnf,status(thm),[intersect_defn])).
% 0.55/0.74 fof(c41,axiom,((![B]:(![C]:(~intersect(B,C)|(?[D]:(member(D,B)&member(D,C))))))&(![B]:(![C]:((![D]:(~member(D,B)|~member(D,C)))|intersect(B,C))))),inference(shift_quantors,status(thm),[c40])).
% 0.55/0.74 fof(c42,axiom,((![X21]:(![X22]:(~intersect(X21,X22)|(?[X23]:(member(X23,X21)&member(X23,X22))))))&(![X24]:(![X25]:((![X26]:(~member(X26,X24)|~member(X26,X25)))|intersect(X24,X25))))),inference(variable_rename,status(thm),[c41])).
% 0.55/0.74 fof(c44,axiom,(![X21]:(![X22]:(![X24]:(![X25]:(![X26]:((~intersect(X21,X22)|(member(skolem0004(X21,X22),X21)&member(skolem0004(X21,X22),X22)))&((~member(X26,X24)|~member(X26,X25))|intersect(X24,X25)))))))),inference(shift_quantors,status(thm),[fof(c43,axiom,((![X21]:(![X22]:(~intersect(X21,X22)|(member(skolem0004(X21,X22),X21)&member(skolem0004(X21,X22),X22)))))&(![X24]:(![X25]:((![X26]:(~member(X26,X24)|~member(X26,X25)))|intersect(X24,X25))))),inference(skolemize,status(esa),[c42])).])).
% 0.55/0.74 fof(c45,axiom,(![X21]:(![X22]:(![X24]:(![X25]:(![X26]:(((~intersect(X21,X22)|member(skolem0004(X21,X22),X21))&(~intersect(X21,X22)|member(skolem0004(X21,X22),X22)))&((~member(X26,X24)|~member(X26,X25))|intersect(X24,X25)))))))),inference(distribute,status(thm),[c44])).
% 0.55/0.74 cnf(c46,axiom,~intersect(X86,X85)|member(skolem0004(X86,X85),X86),inference(split_conjunct,status(thm),[c45])).
% 0.55/0.74 cnf(c93,plain,member(skolem0004(skolem0001,skolem0001),skolem0001)|not_equal(skolem0001,empty_set),inference(resolution,status(thm),[c46, c9])).
% 0.55/0.74 cnf(c327,plain,not_equal(skolem0001,empty_set)|~empty(skolem0001),inference(resolution,status(thm),[c93, c16])).
% 0.55/0.74 cnf(c341,plain,not_equal(skolem0001,empty_set),inference(resolution,status(thm),[c327, c70])).
% 0.55/0.74 cnf(c344,plain,not_equal(empty_set,skolem0001),inference(resolution,status(thm),[c341, c58])).
% 0.55/0.74 cnf(c8,negated_conjecture,~intersect(skolem0001,skolem0001)|~not_equal(skolem0001,empty_set),inference(split_conjunct,status(thm),[c7])).
% 0.55/0.74 cnf(c343,plain,~intersect(skolem0001,skolem0001),inference(resolution,status(thm),[c341, c8])).
% 0.55/0.74 cnf(c48,axiom,~member(X97,X96)|~member(X97,X95)|intersect(X96,X95),inference(split_conjunct,status(thm),[c45])).
% 0.55/0.74 cnf(c97,plain,~member(skolem0002(X235),X236)|intersect(X236,X235)|empty(X235),inference(resolution,status(thm),[c48, c17])).
% 0.55/0.74 cnf(c399,plain,intersect(X237,X237)|empty(X237),inference(resolution,status(thm),[c97, c17])).
% 0.55/0.74 cnf(c403,plain,empty(skolem0001),inference(resolution,status(thm),[c399, c343])).
% 0.55/0.74 fof(equal_member_defn,axiom,(![B]:(![C]:(B=C<=>(![D]:(member(D,B)<=>member(D,C)))))),input).
% 0.55/0.74 fof(c27,axiom,(![B]:(![C]:((B!=C|(![D]:((~member(D,B)|member(D,C))&(~member(D,C)|member(D,B)))))&((?[D]:((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))|B=C)))),inference(fof_nnf,status(thm),[equal_member_defn])).
% 0.55/0.74 fof(c28,axiom,((![B]:(![C]:(B!=C|((![D]:(~member(D,B)|member(D,C)))&(![D]:(~member(D,C)|member(D,B)))))))&(![B]:(![C]:((?[D]:((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))|B=C)))),inference(shift_quantors,status(thm),[c27])).
% 0.55/0.74 fof(c29,axiom,((![X13]:(![X14]:(X13!=X14|((![X15]:(~member(X15,X13)|member(X15,X14)))&(![X16]:(~member(X16,X14)|member(X16,X13)))))))&(![X17]:(![X18]:((?[X19]:((~member(X19,X17)|~member(X19,X18))&(member(X19,X17)|member(X19,X18))))|X17=X18)))),inference(variable_rename,status(thm),[c28])).
% 0.55/0.74 fof(c31,axiom,(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:((X13!=X14|((~member(X15,X13)|member(X15,X14))&(~member(X16,X14)|member(X16,X13))))&(((~member(skolem0003(X17,X18),X17)|~member(skolem0003(X17,X18),X18))&(member(skolem0003(X17,X18),X17)|member(skolem0003(X17,X18),X18)))|X17=X18)))))))),inference(shift_quantors,status(thm),[fof(c30,axiom,((![X13]:(![X14]:(X13!=X14|((![X15]:(~member(X15,X13)|member(X15,X14)))&(![X16]:(~member(X16,X14)|member(X16,X13)))))))&(![X17]:(![X18]:(((~member(skolem0003(X17,X18),X17)|~member(skolem0003(X17,X18),X18))&(member(skolem0003(X17,X18),X17)|member(skolem0003(X17,X18),X18)))|X17=X18)))),inference(skolemize,status(esa),[c29])).])).
% 0.55/0.74 fof(c32,axiom,(![X13]:(![X14]:(![X15]:(![X16]:(![X17]:(![X18]:(((X13!=X14|(~member(X15,X13)|member(X15,X14)))&(X13!=X14|(~member(X16,X14)|member(X16,X13))))&(((~member(skolem0003(X17,X18),X17)|~member(skolem0003(X17,X18),X18))|X17=X18)&((member(skolem0003(X17,X18),X17)|member(skolem0003(X17,X18),X18))|X17=X18))))))))),inference(distribute,status(thm),[c31])).
% 0.55/0.74 cnf(c36,axiom,member(skolem0003(X115,X114),X115)|member(skolem0003(X115,X114),X114)|X115=X114,inference(split_conjunct,status(thm),[c32])).
% 0.55/0.74 cnf(c118,plain,member(skolem0003(empty_set,X306),X306)|empty_set=X306,inference(resolution,status(thm),[c36, c39])).
% 0.55/0.74 cnf(c603,plain,empty_set=X307|~empty(X307),inference(resolution,status(thm),[c118, c16])).
% 0.55/0.74 cnf(c631,plain,empty_set=skolem0001,inference(resolution,status(thm),[c603, c403])).
% 0.55/0.74 cnf(c653,plain,~not_equal(empty_set,skolem0001),inference(resolution,status(thm),[c631, c25])).
% 0.55/0.74 cnf(c670,plain,$false,inference(resolution,status(thm),[c653, c344])).
% 0.55/0.74 # SZS output end CNFRefutation
% 0.55/0.74
% 0.55/0.74 # Initial clauses : 22
% 0.55/0.74 # Processed clauses : 87
% 0.55/0.74 # Factors computed : 15
% 0.55/0.74 # Resolvents computed: 641
% 0.55/0.74 # Tautologies deleted: 6
% 0.55/0.74 # Forward subsumed : 105
% 0.55/0.74 # Backward subsumed : 9
% 0.55/0.74 # -------- CPU Time ---------
% 0.55/0.74 # User time : 0.376 s
% 0.55/0.74 # System time : 0.011 s
% 0.55/0.74 # Total time : 0.387 s
%------------------------------------------------------------------------------