TSTP Solution File: CSR042+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CSR042+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 21:41:16 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% 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 : CSR042+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
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 12:19:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.42 Command-line arguments: --no-flatten-goal
% 0.21/0.42
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Take the following subset of the input axioms:
% 0.21/0.43 fof(just1, axiom, mtvisible(c_tptpgeo_member7_mt) => borderson(c_georegion_l4_x27_y64, c_georegion_l4_x27_y65)).
% 0.21/0.43 fof(just2, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.21/0.43 fof(just28, axiom, ![X, Y]: (borderson(X, Y) => borderson(Y, X))).
% 0.21/0.43 fof(just29, axiom, ![X2]: ~borderson(X2, X2)).
% 0.21/0.43 fof(query42, conjecture, ?[ARG1]: (mtvisible(c_tptpgeo_member7_mt) => borderson(ARG1, c_georegion_l4_x27_y64))).
% 0.21/0.43
% 0.21/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.43 fresh(y, y, x1...xn) = u
% 0.21/0.43 C => fresh(s, t, x1...xn) = v
% 0.21/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.43 variables of u and v.
% 0.21/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.43 input problem has no model of domain size 1).
% 0.21/0.43
% 0.21/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.43
% 0.21/0.43 Axiom 1 (query42): mtvisible(c_tptpgeo_member7_mt) = true2.
% 0.21/0.43 Axiom 2 (just1): fresh32(X, X) = true2.
% 0.21/0.43 Axiom 3 (just1): fresh32(mtvisible(c_tptpgeo_member7_mt), true2) = borderson(c_georegion_l4_x27_y64, c_georegion_l4_x27_y65).
% 0.21/0.43 Axiom 4 (just28): fresh10(X, X, Y, Z) = true2.
% 0.21/0.43 Axiom 5 (just28): fresh10(borderson(X, Y), true2, X, Y) = borderson(Y, X).
% 0.21/0.43
% 0.21/0.43 Goal 1 (query42_1): borderson(X, c_georegion_l4_x27_y64) = true2.
% 0.21/0.43 The goal is true when:
% 0.21/0.43 X = c_georegion_l4_x27_y65
% 0.21/0.43
% 0.21/0.43 Proof:
% 0.21/0.43 borderson(c_georegion_l4_x27_y65, c_georegion_l4_x27_y64)
% 0.21/0.43 = { by axiom 5 (just28) R->L }
% 0.21/0.43 fresh10(borderson(c_georegion_l4_x27_y64, c_georegion_l4_x27_y65), true2, c_georegion_l4_x27_y64, c_georegion_l4_x27_y65)
% 0.21/0.43 = { by axiom 3 (just1) R->L }
% 0.21/0.43 fresh10(fresh32(mtvisible(c_tptpgeo_member7_mt), true2), true2, c_georegion_l4_x27_y64, c_georegion_l4_x27_y65)
% 0.21/0.43 = { by axiom 1 (query42) }
% 0.21/0.43 fresh10(fresh32(true2, true2), true2, c_georegion_l4_x27_y64, c_georegion_l4_x27_y65)
% 0.21/0.43 = { by axiom 2 (just1) }
% 0.21/0.43 fresh10(true2, true2, c_georegion_l4_x27_y64, c_georegion_l4_x27_y65)
% 0.21/0.43 = { by axiom 4 (just28) }
% 0.21/0.43 true2
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Theorem (the conjecture is true).
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