0.04/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.15 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.14/0.37 % Computer : n005.cluster.edu 0.14/0.37 % Model : x86_64 x86_64 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.37 % Memory : 8042.1875MB 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.37 % CPULimit : 180 0.14/0.37 % DateTime : Thu Aug 29 09:35:48 EDT 2019 0.14/0.37 % CPUTime : 0.22/0.50 % SZS status Unsatisfiable 0.22/0.50 0.22/0.50 % SZS output start Proof 0.22/0.50 Take the following subset of the input axioms: 0.22/0.50 fof(goal, negated_conjecture, b!=a). 0.22/0.50 fof(ifeq_axiom, axiom, ![A, B, C]: ifeq3(A, A, B, C)=B). 0.22/0.50 fof(ifeq_axiom_001, axiom, ![A, B, C]: B=ifeq2(A, A, B, C)). 0.22/0.50 fof(just1, axiom, ![TERM, PRED, INDEPCOL, DEPCOL]: true=ifeq3(relationallexists(PRED, INDEPCOL, DEPCOL), true, ifeq3(isa(TERM, INDEPCOL), true, isa(f_relationallexistsfn(TERM, PRED, INDEPCOL, DEPCOL), DEPCOL), true), true)). 0.22/0.50 fof(just12, axiom, ![TERM]: ifeq3(mtvisible(c_tptp_member2610_mt), true, ifeq3(isa(TERM, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, tptp_8_875(TERM, f_relationallexistsfn(TERM, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), true)=true). 0.22/0.50 fof(just13, axiom, ifeq3(mtvisible(c_tptp_member2610_mt), true, relationallexists(c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), true)=true). 0.22/0.50 fof(just14, axiom, isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent))=true). 0.22/0.50 fof(just34, axiom, ![X]: true=ifeq3(isa(X, c_tptpcol_16_31868), true, tptpcol_16_31868(X), true)). 0.22/0.50 fof(just63, axiom, ![SPECMT, GENLMT]: true=ifeq3(genlmt(SPECMT, GENLMT), true, ifeq3(mtvisible(SPECMT), true, mtvisible(GENLMT), true), true)). 0.22/0.50 fof(just9, axiom, genlmt(c_tptp_spindlecollectormt, c_tptp_member2610_mt)=true). 0.22/0.50 fof(query27, negated_conjecture, true=mtvisible(c_tptp_spindlecollectormt)). 0.22/0.50 fof(query27_1, negated_conjecture, ![X]: ifeq2(tuple2(tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, X), tptpcol_16_31868(X)), tuple2(true, true), a, b)=b). 0.22/0.50 0.22/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of 0.22/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 0.22/0.50 We repeatedly replace C & s=t => u=v by the two clauses: 0.22/0.50 fresh(y, y, x1...xn) = u 0.22/0.50 C => fresh(s, t, x1...xn) = v 0.22/0.50 where fresh is a fresh function symbol and x1..xn are the free 0.22/0.50 variables of u and v. 0.22/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the 0.22/0.50 input problem has no model of domain size 1). 0.22/0.50 0.22/0.50 The encoding turns the above axioms into the following unit equations and goals: 0.22/0.50 0.22/0.50 Axiom 1 (just63): true = ifeq3(genlmt(X, Y), true, ifeq3(mtvisible(X), true, mtvisible(Y), true), true). 0.22/0.50 Axiom 2 (query27): true = mtvisible(c_tptp_spindlecollectormt). 0.22/0.50 Axiom 3 (ifeq_axiom_001): X = ifeq2(Y, Y, X, Z). 0.22/0.50 Axiom 4 (just9): genlmt(c_tptp_spindlecollectormt, c_tptp_member2610_mt) = true. 0.22/0.50 Axiom 5 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y. 0.22/0.50 Axiom 6 (just13): ifeq3(mtvisible(c_tptp_member2610_mt), true, relationallexists(c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), true) = true. 0.22/0.50 Axiom 7 (just14): isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)) = true. 0.22/0.50 Axiom 8 (just1): true = ifeq3(relationallexists(X, Y, Z), true, ifeq3(isa(W, Y), true, isa(f_relationallexistsfn(W, X, Y, Z), Z), true), true). 0.22/0.50 Axiom 9 (query27_1): ifeq2(tuple2(tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, X), tptpcol_16_31868(X)), tuple2(true, true), a, b) = b. 0.22/0.50 Axiom 10 (just12): ifeq3(mtvisible(c_tptp_member2610_mt), true, ifeq3(isa(X, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, tptp_8_875(X, f_relationallexistsfn(X, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), true) = true. 0.22/0.50 Axiom 11 (just34): true = ifeq3(isa(X, c_tptpcol_16_31868), true, tptpcol_16_31868(X), true). 0.22/0.50 0.22/0.50 Lemma 12: mtvisible(c_tptp_member2610_mt) = true. 0.22/0.50 Proof: 0.22/0.50 mtvisible(c_tptp_member2610_mt) 0.22/0.50 = { by axiom 5 (ifeq_axiom) } 0.22/0.50 ifeq3(true, true, mtvisible(c_tptp_member2610_mt), true) 0.22/0.50 = { by axiom 2 (query27) } 0.22/0.50 ifeq3(mtvisible(c_tptp_spindlecollectormt), true, mtvisible(c_tptp_member2610_mt), true) 0.22/0.50 = { by axiom 5 (ifeq_axiom) } 0.22/0.50 ifeq3(true, true, ifeq3(mtvisible(c_tptp_spindlecollectormt), true, mtvisible(c_tptp_member2610_mt), true), true) 0.22/0.50 = { by axiom 4 (just9) } 0.22/0.50 ifeq3(genlmt(c_tptp_spindlecollectormt, c_tptp_member2610_mt), true, ifeq3(mtvisible(c_tptp_spindlecollectormt), true, mtvisible(c_tptp_member2610_mt), true), true) 0.22/0.50 = { by axiom 1 (just63) } 0.22/0.52 true 0.22/0.52 0.22/0.52 Goal 1 (goal): b = a. 0.22/0.52 Proof: 0.22/0.52 b 0.22/0.52 = { by axiom 9 (query27_1) } 0.22/0.52 ifeq2(tuple2(tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 5 (ifeq_axiom) } 0.22/0.52 ifeq2(tuple2(ifeq3(true, true, tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by lemma 12 } 0.22/0.52 ifeq2(tuple2(ifeq3(mtvisible(c_tptp_member2610_mt), true, tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 5 (ifeq_axiom) } 0.22/0.52 ifeq2(tuple2(ifeq3(mtvisible(c_tptp_member2610_mt), true, ifeq3(true, true, tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), true), tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 7 (just14) } 0.22/0.52 ifeq2(tuple2(ifeq3(mtvisible(c_tptp_member2610_mt), true, ifeq3(isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, tptp_8_875(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true), true), tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 10 (just12) } 0.22/0.52 ifeq2(tuple2(true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868))), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 5 (ifeq_axiom) } 0.22/0.52 ifeq2(tuple2(true, ifeq3(true, true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.22/0.52 = { by axiom 8 (just1) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(relationallexists(c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), true, ifeq3(isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 5 (ifeq_axiom) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(ifeq3(true, true, relationallexists(c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), true), true, ifeq3(isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by lemma 12 } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(ifeq3(mtvisible(c_tptp_member2610_mt), true, relationallexists(c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), true), true, ifeq3(isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 6 (just13) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(true, true, ifeq3(isa(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent)), true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 7 (just14) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(true, true, ifeq3(true, true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 5 (ifeq_axiom) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(ifeq3(true, true, isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 5 (ifeq_axiom) } 0.35/0.52 ifeq2(tuple2(true, ifeq3(isa(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868), c_tptpcol_16_31868), true, tptpcol_16_31868(f_relationallexistsfn(c_tptpnsubcollectionofwithrelationfromtypefnunitvectorintervaldirectionoftranslation_throughoutmovement_translationevent_786, c_tptp_8_875, f_subcollectionofwithrelationfromtypefn(c_unitvectorinterval, c_directionoftranslation_throughout, c_movement_translationevent), c_tptpcol_16_31868)), true)), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 11 (just34) } 0.35/0.52 ifeq2(tuple2(true, true), tuple2(true, true), a, b) 0.35/0.52 = { by axiom 3 (ifeq_axiom_001) } 0.35/0.52 a 0.35/0.52 % SZS output end Proof 0.35/0.52 0.35/0.52 RESULT: Unsatisfiable (the axioms are contradictory). 0.35/0.52 EOF