TSTP Solution File: PUZ003-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ003-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n029.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 : Thu Aug 31 13:23:52 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% 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
% 0.00/0.12 % Problem : PUZ003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 22:46:40 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Take the following subset of the input axioms:
% 0.20/0.39 fof(all_shaved_then_one_shaved, axiom, ![X, Y]: (~shaved(members, X) | (~member(Y) | shaved(Y, X)))).
% 0.20/0.39 fof(cesare, hypothesis, member(cesare)).
% 0.20/0.39 fof(guido, hypothesis, member(guido)).
% 0.20/0.39 fof(guido_has_shaved_cesare, hypothesis, shaved(guido, cesare)).
% 0.20/0.39 fof(lorenzo, hypothesis, member(lorenzo)).
% 0.20/0.39 fof(one_shaved_then_all_shaved, axiom, ![X2, Y2]: (~member(X2) | (~member(Y2) | (~shaved(X2, Y2) | shaved(members, X2))))).
% 0.20/0.39 fof(petruchio, hypothesis, member(petruchio)).
% 0.20/0.39 fof(prove_petruchio_has_shaved_lorenzo, negated_conjecture, ~shaved(petruchio, lorenzo)).
% 0.20/0.39
% 0.20/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39 fresh(y, y, x1...xn) = u
% 0.20/0.39 C => fresh(s, t, x1...xn) = v
% 0.20/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39 variables of u and v.
% 0.20/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39 input problem has no model of domain size 1).
% 0.20/0.39
% 0.20/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39
% 0.20/0.39 Axiom 1 (lorenzo): member(lorenzo) = true.
% 0.20/0.39 Axiom 2 (petruchio): member(petruchio) = true.
% 0.20/0.39 Axiom 3 (guido): member(guido) = true.
% 0.20/0.39 Axiom 4 (cesare): member(cesare) = true.
% 0.20/0.39 Axiom 5 (guido_has_shaved_cesare): shaved(guido, cesare) = true.
% 0.20/0.39 Axiom 6 (one_shaved_then_all_shaved): fresh(X, X, Y) = shaved(members, Y).
% 0.20/0.39 Axiom 7 (one_shaved_then_all_shaved): fresh5(X, X, Y) = true.
% 0.20/0.39 Axiom 8 (one_shaved_then_all_shaved): fresh4(X, X, Y, Z) = fresh5(member(Y), true, Y).
% 0.20/0.39 Axiom 9 (all_shaved_then_one_shaved): fresh3(X, X, Y, Z) = true.
% 0.20/0.39 Axiom 10 (all_shaved_then_one_shaved): fresh2(X, X, Y, Z) = shaved(Z, Y).
% 0.20/0.39 Axiom 11 (one_shaved_then_all_shaved): fresh4(shaved(X, Y), true, X, Y) = fresh(member(Y), true, X).
% 0.20/0.39 Axiom 12 (all_shaved_then_one_shaved): fresh2(shaved(members, X), true, X, Y) = fresh3(member(Y), true, X, Y).
% 0.20/0.39
% 0.20/0.39 Goal 1 (prove_petruchio_has_shaved_lorenzo): shaved(petruchio, lorenzo) = true.
% 0.20/0.39 Proof:
% 0.20/0.39 shaved(petruchio, lorenzo)
% 0.20/0.39 = { by axiom 10 (all_shaved_then_one_shaved) R->L }
% 0.20/0.39 fresh2(true, true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 7 (one_shaved_then_all_shaved) R->L }
% 0.20/0.39 fresh2(fresh5(true, true, lorenzo), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 1 (lorenzo) R->L }
% 0.20/0.39 fresh2(fresh5(member(lorenzo), true, lorenzo), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 8 (one_shaved_then_all_shaved) R->L }
% 0.20/0.39 fresh2(fresh4(true, true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 9 (all_shaved_then_one_shaved) R->L }
% 0.20/0.39 fresh2(fresh4(fresh3(true, true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 1 (lorenzo) R->L }
% 0.20/0.39 fresh2(fresh4(fresh3(member(lorenzo), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 12 (all_shaved_then_one_shaved) R->L }
% 0.20/0.39 fresh2(fresh4(fresh2(shaved(members, guido), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 6 (one_shaved_then_all_shaved) R->L }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh(true, true, guido), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 4 (cesare) R->L }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh(member(cesare), true, guido), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 11 (one_shaved_then_all_shaved) R->L }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh4(shaved(guido, cesare), true, guido, cesare), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 5 (guido_has_shaved_cesare) }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh4(true, true, guido, cesare), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 8 (one_shaved_then_all_shaved) }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh5(member(guido), true, guido), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 3 (guido) }
% 0.20/0.39 fresh2(fresh4(fresh2(fresh5(true, true, guido), true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 7 (one_shaved_then_all_shaved) }
% 0.20/0.39 fresh2(fresh4(fresh2(true, true, guido, lorenzo), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 10 (all_shaved_then_one_shaved) }
% 0.20/0.39 fresh2(fresh4(shaved(lorenzo, guido), true, lorenzo, guido), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 11 (one_shaved_then_all_shaved) }
% 0.20/0.39 fresh2(fresh(member(guido), true, lorenzo), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 3 (guido) }
% 0.20/0.39 fresh2(fresh(true, true, lorenzo), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 6 (one_shaved_then_all_shaved) }
% 0.20/0.39 fresh2(shaved(members, lorenzo), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 12 (all_shaved_then_one_shaved) }
% 0.20/0.39 fresh3(member(petruchio), true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 2 (petruchio) }
% 0.20/0.39 fresh3(true, true, lorenzo, petruchio)
% 0.20/0.39 = { by axiom 9 (all_shaved_then_one_shaved) }
% 0.20/0.39 true
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39
% 0.20/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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