TSTP Solution File: CSR030+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR030+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n013.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 : 300s
% DateTime : Wed Aug 30 21:41:05 EDT 2023
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR030+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.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 : 300
% 0.13/0.34 % DateTime : Mon Aug 28 13:41:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Command-line arguments: --no-flatten-goal
% 0.20/0.46
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Take the following subset of the input axioms:
% 0.20/0.47 fof(just11, axiom, genlmt(c_tptp_member3393_mt, c_tptp_spindleheadmt)).
% 0.20/0.47 fof(just12, axiom, mtvisible(c_tptp_spindleheadmt) => tptptypes_7_389(c_pushingwithopenhand, c_tptpcol_16_4451)).
% 0.20/0.47 fof(just13, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.20/0.47 fof(just49, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))).
% 0.20/0.47 fof(just7, axiom, ![ARG1, ARG2]: (tptptypes_6_388(ARG1, ARG2) => tptptypes_5_387(ARG1, ARG2))).
% 0.20/0.47 fof(just9, axiom, ![ARG2_2, ARG1_2]: (tptptypes_7_389(ARG1_2, ARG2_2) => tptptypes_6_388(ARG2_2, ARG1_2))).
% 0.20/0.47 fof(query30, conjecture, ?[ARG2_2]: (mtvisible(c_tptp_member3393_mt) => tptptypes_5_387(ARG2_2, c_pushingwithopenhand))).
% 0.20/0.47
% 0.20/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.47 fresh(y, y, x1...xn) = u
% 0.20/0.47 C => fresh(s, t, x1...xn) = v
% 0.20/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.47 variables of u and v.
% 0.20/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.47 input problem has no model of domain size 1).
% 0.20/0.47
% 0.20/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.47
% 0.20/0.47 Axiom 1 (query30): mtvisible(c_tptp_member3393_mt) = true2.
% 0.20/0.47 Axiom 2 (just12): fresh53(X, X) = true2.
% 0.20/0.47 Axiom 3 (just11): genlmt(c_tptp_member3393_mt, c_tptp_spindleheadmt) = true2.
% 0.20/0.47 Axiom 4 (just12): fresh53(mtvisible(c_tptp_spindleheadmt), true2) = tptptypes_7_389(c_pushingwithopenhand, c_tptpcol_16_4451).
% 0.20/0.47 Axiom 5 (just49): fresh11(X, X, Y) = true2.
% 0.20/0.47 Axiom 6 (just9): fresh(X, X, Y, Z) = true2.
% 0.20/0.47 Axiom 7 (just49): fresh12(X, X, Y, Z) = mtvisible(Z).
% 0.20/0.47 Axiom 8 (just7): fresh2(X, X, Y, Z) = true2.
% 0.20/0.47 Axiom 9 (just49): fresh12(mtvisible(X), true2, X, Y) = fresh11(genlmt(X, Y), true2, Y).
% 0.20/0.47 Axiom 10 (just9): fresh(tptptypes_7_389(X, Y), true2, X, Y) = tptptypes_6_388(Y, X).
% 0.20/0.47 Axiom 11 (just7): fresh2(tptptypes_6_388(X, Y), true2, X, Y) = tptptypes_5_387(X, Y).
% 0.20/0.47
% 0.20/0.47 Goal 1 (query30_1): tptptypes_5_387(X, c_pushingwithopenhand) = true2.
% 0.20/0.47 The goal is true when:
% 0.20/0.47 X = c_tptpcol_16_4451
% 0.20/0.47
% 0.20/0.47 Proof:
% 0.20/0.47 tptptypes_5_387(c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 11 (just7) R->L }
% 0.20/0.47 fresh2(tptptypes_6_388(c_tptpcol_16_4451, c_pushingwithopenhand), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 10 (just9) R->L }
% 0.20/0.47 fresh2(fresh(tptptypes_7_389(c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 4 (just12) R->L }
% 0.20/0.47 fresh2(fresh(fresh53(mtvisible(c_tptp_spindleheadmt), true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 7 (just49) R->L }
% 0.20/0.47 fresh2(fresh(fresh53(fresh12(true2, true2, c_tptp_member3393_mt, c_tptp_spindleheadmt), true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 1 (query30) R->L }
% 0.20/0.47 fresh2(fresh(fresh53(fresh12(mtvisible(c_tptp_member3393_mt), true2, c_tptp_member3393_mt, c_tptp_spindleheadmt), true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 9 (just49) }
% 0.20/0.47 fresh2(fresh(fresh53(fresh11(genlmt(c_tptp_member3393_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt), true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 3 (just11) }
% 0.20/0.47 fresh2(fresh(fresh53(fresh11(true2, true2, c_tptp_spindleheadmt), true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 5 (just49) }
% 0.20/0.47 fresh2(fresh(fresh53(true2, true2), true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 2 (just12) }
% 0.20/0.47 fresh2(fresh(true2, true2, c_pushingwithopenhand, c_tptpcol_16_4451), true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 6 (just9) }
% 0.20/0.47 fresh2(true2, true2, c_tptpcol_16_4451, c_pushingwithopenhand)
% 0.20/0.47 = { by axiom 8 (just7) }
% 0.20/0.47 true2
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47
% 0.20/0.47 RESULT: Theorem (the conjecture is true).
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