TSTP Solution File: CSR031+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CSR031+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 : n019.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 21:41:06 EDT 2023
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR031+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 11:18:28 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.46 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.46
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 Take the following subset of the input axioms:
% 0.19/0.46 fof(just11, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.19/0.46 fof(just34, axiom, ![ARG2, INS]: (disjointwith(INS, ARG2) => collection(INS))).
% 0.19/0.46 fof(just4, axiom, ![OBJ2]: ~(collection(OBJ2) & individual(OBJ2))).
% 0.19/0.46 fof(just6, axiom, individual(c_tptptptpcol_16_8398)).
% 0.19/0.46 fof(just7, axiom, ![OBJ2, COL1_2, COL2_2]: ~(isa(OBJ2, COL1_2) & (isa(OBJ2, COL2_2) & disjointwith(COL1_2, COL2_2)))).
% 0.19/0.46 fof(query31, conjecture, ~disjointwith(c_tptptptpcol_16_8398, c_tptpcol_16_18488)).
% 0.19/0.46
% 0.19/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.46 fresh(y, y, x1...xn) = u
% 0.19/0.46 C => fresh(s, t, x1...xn) = v
% 0.19/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.46 variables of u and v.
% 0.19/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.46 input problem has no model of domain size 1).
% 0.19/0.46
% 0.19/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.46
% 0.19/0.46 Axiom 1 (just6): individual(c_tptptptpcol_16_8398) = true2.
% 0.19/0.46 Axiom 2 (query31): disjointwith(c_tptptptpcol_16_8398, c_tptpcol_16_18488) = true2.
% 0.19/0.46 Axiom 3 (just34): fresh26(X, X, Y) = true2.
% 0.19/0.46 Axiom 4 (just34): fresh26(disjointwith(X, Y), true2, X) = collection(X).
% 0.19/0.46
% 0.19/0.46 Goal 1 (just4): tuple2(collection(X), individual(X)) = tuple2(true2, true2).
% 0.19/0.46 The goal is true when:
% 0.19/0.46 X = c_tptptptpcol_16_8398
% 0.19/0.46
% 0.19/0.46 Proof:
% 0.19/0.46 tuple2(collection(c_tptptptpcol_16_8398), individual(c_tptptptpcol_16_8398))
% 0.19/0.46 = { by axiom 4 (just34) R->L }
% 0.19/0.46 tuple2(fresh26(disjointwith(c_tptptptpcol_16_8398, c_tptpcol_16_18488), true2, c_tptptptpcol_16_8398), individual(c_tptptptpcol_16_8398))
% 0.19/0.46 = { by axiom 2 (query31) }
% 0.19/0.46 tuple2(fresh26(true2, true2, c_tptptptpcol_16_8398), individual(c_tptptptpcol_16_8398))
% 0.19/0.46 = { by axiom 3 (just34) }
% 0.19/0.46 tuple2(true2, individual(c_tptptptpcol_16_8398))
% 0.19/0.46 = { by axiom 1 (just6) }
% 0.19/0.46 tuple2(true2, true2)
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Theorem (the conjecture is true).
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