TSTP Solution File: COM003-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM003-2 : TPTP v8.1.2. Released v1.1.0.
% 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 : n018.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 18:45:18 EDT 2023
% Result : Unsatisfiable 0.20s 0.49s
% 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
% 0.08/0.13 % Problem : COM003-2 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 13:10:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Take the following subset of the input axioms:
% 0.20/0.49 fof(axiom1_1, hypothesis, ![X]: (~algorithm_program_decides(X) | program_program_decides(c1))).
% 0.20/0.49 fof(axiom2_1, hypothesis, ![Y, Z, W]: (~program_program_decides(W) | program_halts2_halts3_outputs(W, Y, Z, good))).
% 0.20/0.49 fof(axiom2_2, hypothesis, ![Y2, Z2, W2]: (~program_program_decides(W2) | program_not_halts2_halts3_outputs(W2, Y2, Z2, bad))).
% 0.20/0.49 fof(program_halts2_halts3_outputs1, axiom, ![X2, Y2, Z2, W2]: (~program_halts2_halts3_outputs(X2, Y2, Z2, W2) | program_halts2(Y2, Z2))).
% 0.20/0.49 fof(program_halts3a, axiom, ![X2, Y2]: (~program_halts2(X2, Y2) | halts2(X2, Y2))).
% 0.20/0.49 fof(program_not_halts2_halts3_outputs1, axiom, ![X2, Y2, Z2, W2]: (~program_not_halts2_halts3_outputs(X2, Y2, Z2, W2) | program_not_halts2(Y2, Z2))).
% 0.20/0.49 fof(program_not_halts3a, axiom, ![X2, Y2]: (~program_not_halts2(X2, Y2) | ~halts2(X2, Y2))).
% 0.20/0.49 fof(prove_algorithm_does_not_exist, negated_conjecture, algorithm_program_decides(c4)).
% 0.20/0.49
% 0.20/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49 fresh(y, y, x1...xn) = u
% 0.20/0.49 C => fresh(s, t, x1...xn) = v
% 0.20/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49 variables of u and v.
% 0.20/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49 input problem has no model of domain size 1).
% 0.20/0.49
% 0.20/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49
% 0.20/0.49 Axiom 1 (prove_algorithm_does_not_exist): algorithm_program_decides(c4) = true2.
% 0.20/0.49 Axiom 2 (axiom1_1): fresh44(X, X) = true2.
% 0.20/0.49 Axiom 3 (axiom1_1): fresh44(algorithm_program_decides(X), true2) = program_program_decides(c1).
% 0.20/0.49 Axiom 4 (program_halts2_halts3_outputs1): fresh20(X, X, Y, Z) = true2.
% 0.20/0.49 Axiom 5 (program_halts3a): fresh16(X, X, Y, Z) = true2.
% 0.20/0.49 Axiom 6 (program_not_halts2_halts3_outputs1): fresh8(X, X, Y, Z) = true2.
% 0.20/0.49 Axiom 7 (axiom2_1): fresh43(X, X, Y, Z, W) = true2.
% 0.20/0.49 Axiom 8 (axiom2_2): fresh42(X, X, Y, Z, W) = true2.
% 0.20/0.49 Axiom 9 (axiom2_1): fresh43(program_program_decides(X), true2, X, Y, Z) = program_halts2_halts3_outputs(X, Y, Z, good).
% 0.20/0.49 Axiom 10 (axiom2_2): fresh42(program_program_decides(X), true2, X, Y, Z) = program_not_halts2_halts3_outputs(X, Y, Z, bad).
% 0.20/0.49 Axiom 11 (program_halts3a): fresh16(program_halts2(X, Y), true2, X, Y) = halts2(X, Y).
% 0.20/0.49 Axiom 12 (program_halts2_halts3_outputs1): fresh20(program_halts2_halts3_outputs(X, Y, Z, W), true2, Y, Z) = program_halts2(Y, Z).
% 0.20/0.49 Axiom 13 (program_not_halts2_halts3_outputs1): fresh8(program_not_halts2_halts3_outputs(X, Y, Z, W), true2, Y, Z) = program_not_halts2(Y, Z).
% 0.20/0.49
% 0.20/0.49 Lemma 14: program_program_decides(c1) = true2.
% 0.20/0.49 Proof:
% 0.20/0.49 program_program_decides(c1)
% 0.20/0.49 = { by axiom 3 (axiom1_1) R->L }
% 0.20/0.49 fresh44(algorithm_program_decides(c4), true2)
% 0.20/0.49 = { by axiom 1 (prove_algorithm_does_not_exist) }
% 0.20/0.49 fresh44(true2, true2)
% 0.20/0.49 = { by axiom 2 (axiom1_1) }
% 0.20/0.50 true2
% 0.20/0.50
% 0.20/0.50 Goal 1 (program_not_halts3a): tuple(halts2(X, Y), program_not_halts2(X, Y)) = tuple(true2, true2).
% 0.20/0.50 The goal is true when:
% 0.20/0.50 X = X
% 0.20/0.50 Y = Y
% 0.20/0.50
% 0.20/0.50 Proof:
% 0.20/0.50 tuple(halts2(X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 11 (program_halts3a) R->L }
% 0.20/0.50 tuple(fresh16(program_halts2(X, Y), true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 12 (program_halts2_halts3_outputs1) R->L }
% 0.20/0.50 tuple(fresh16(fresh20(program_halts2_halts3_outputs(c1, X, Y, good), true2, X, Y), true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 9 (axiom2_1) R->L }
% 0.20/0.50 tuple(fresh16(fresh20(fresh43(program_program_decides(c1), true2, c1, X, Y), true2, X, Y), true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by lemma 14 }
% 0.20/0.50 tuple(fresh16(fresh20(fresh43(true2, true2, c1, X, Y), true2, X, Y), true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 7 (axiom2_1) }
% 0.20/0.50 tuple(fresh16(fresh20(true2, true2, X, Y), true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 4 (program_halts2_halts3_outputs1) }
% 0.20/0.50 tuple(fresh16(true2, true2, X, Y), program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 5 (program_halts3a) }
% 0.20/0.50 tuple(true2, program_not_halts2(X, Y))
% 0.20/0.50 = { by axiom 13 (program_not_halts2_halts3_outputs1) R->L }
% 0.20/0.50 tuple(true2, fresh8(program_not_halts2_halts3_outputs(c1, X, Y, bad), true2, X, Y))
% 0.20/0.50 = { by axiom 10 (axiom2_2) R->L }
% 0.20/0.50 tuple(true2, fresh8(fresh42(program_program_decides(c1), true2, c1, X, Y), true2, X, Y))
% 0.20/0.50 = { by lemma 14 }
% 0.20/0.50 tuple(true2, fresh8(fresh42(true2, true2, c1, X, Y), true2, X, Y))
% 0.20/0.50 = { by axiom 8 (axiom2_2) }
% 0.20/0.50 tuple(true2, fresh8(true2, true2, X, Y))
% 0.20/0.50 = { by axiom 6 (program_not_halts2_halts3_outputs1) }
% 0.20/0.50 tuple(true2, true2)
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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