TSTP Solution File: LCL203-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL203-1 : 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 : n027.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 08:17:58 EDT 2023
% Result : Unsatisfiable 2.32s 0.88s
% Output : Proof 2.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL203-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 07:27:03 EDT 2023
% 0.12/0.33 % CPUTime :
% 2.32/0.88 Command-line arguments: --ground-connectedness --complete-subsets
% 2.32/0.88
% 2.32/0.88 % SZS status Unsatisfiable
% 2.32/0.88
% 2.32/0.89 % SZS output start Proof
% 2.32/0.89 Take the following subset of the input axioms:
% 2.32/0.89 fof(axiom_1_2, axiom, ![A]: axiom(or(not(or(A, A)), A))).
% 2.32/0.89 fof(axiom_1_3, axiom, ![B, A2]: axiom(or(not(A2), or(B, A2)))).
% 2.32/0.89 fof(axiom_1_4, axiom, ![A2, B2]: axiom(or(not(or(A2, B2)), or(B2, A2)))).
% 2.32/0.89 fof(axiom_1_5, axiom, ![C, A2, B2]: axiom(or(not(or(A2, or(B2, C))), or(B2, or(A2, C))))).
% 2.32/0.89 fof(prove_this, negated_conjecture, ~theorem(or(not(not(or(p, q))), or(not(p), not(q))))).
% 2.32/0.89 fof(rule_1, axiom, ![X]: (theorem(X) | ~axiom(X))).
% 2.32/0.89 fof(rule_2, axiom, ![Y, X2]: (theorem(X2) | (~axiom(or(not(Y), X2)) | ~theorem(Y)))).
% 2.32/0.89 fof(rule_3, axiom, ![Z, X2, Y2]: (theorem(or(not(X2), Z)) | (~axiom(or(not(X2), Y2)) | ~theorem(or(not(Y2), Z))))).
% 2.32/0.89
% 2.32/0.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.32/0.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.32/0.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.32/0.89 fresh(y, y, x1...xn) = u
% 2.32/0.89 C => fresh(s, t, x1...xn) = v
% 2.32/0.89 where fresh is a fresh function symbol and x1..xn are the free
% 2.32/0.89 variables of u and v.
% 2.32/0.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.32/0.89 input problem has no model of domain size 1).
% 2.32/0.89
% 2.32/0.89 The encoding turns the above axioms into the following unit equations and goals:
% 2.32/0.89
% 2.32/0.89 Axiom 1 (rule_1): fresh4(X, X, Y) = true.
% 2.32/0.89 Axiom 2 (rule_2): fresh3(X, X, Y) = true.
% 2.32/0.89 Axiom 3 (rule_3): fresh(X, X, Y, Z) = true.
% 2.32/0.89 Axiom 4 (rule_2): fresh5(X, X, Y, Z) = theorem(Y).
% 2.32/0.89 Axiom 5 (rule_1): fresh4(axiom(X), true, X) = theorem(X).
% 2.32/0.89 Axiom 6 (rule_3): fresh2(X, X, Y, Z, W) = theorem(or(not(Y), Z)).
% 2.32/0.89 Axiom 7 (axiom_1_3): axiom(or(not(X), or(Y, X))) = true.
% 2.32/0.89 Axiom 8 (axiom_1_2): axiom(or(not(or(X, X)), X)) = true.
% 2.32/0.89 Axiom 9 (rule_2): fresh5(theorem(X), true, Y, X) = fresh3(axiom(or(not(X), Y)), true, Y).
% 2.32/0.89 Axiom 10 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 2.32/0.89 Axiom 11 (rule_3): fresh2(theorem(or(not(X), Y)), true, Z, Y, X) = fresh(axiom(or(not(Z), X)), true, Z, Y).
% 2.32/0.89 Axiom 12 (axiom_1_5): axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))) = true.
% 2.32/0.89
% 2.32/0.89 Lemma 13: fresh5(theorem(or(X, Y)), true, or(Y, X), or(X, Y)) = true.
% 2.32/0.89 Proof:
% 2.32/0.89 fresh5(theorem(or(X, Y)), true, or(Y, X), or(X, Y))
% 2.32/0.89 = { by axiom 9 (rule_2) }
% 2.32/0.89 fresh3(axiom(or(not(or(X, Y)), or(Y, X))), true, or(Y, X))
% 2.32/0.89 = { by axiom 10 (axiom_1_4) }
% 2.32/0.89 fresh3(true, true, or(Y, X))
% 2.32/0.89 = { by axiom 2 (rule_2) }
% 2.32/0.89 true
% 2.32/0.89
% 2.32/0.89 Goal 1 (prove_this): theorem(or(not(not(or(p, q))), or(not(p), not(q)))) = true.
% 2.32/0.89 Proof:
% 2.32/0.89 theorem(or(not(not(or(p, q))), or(not(p), not(q))))
% 2.32/0.89 = { by axiom 4 (rule_2) R->L }
% 2.32/0.89 fresh5(true, true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 2 (rule_2) R->L }
% 2.32/0.89 fresh5(fresh3(true, true, or(not(p), or(not(not(or(p, q))), not(q)))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 7 (axiom_1_3) R->L }
% 2.32/0.89 fresh5(fresh3(axiom(or(not(or(not(not(or(p, q))), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))), true, or(not(p), or(not(not(or(p, q))), not(q)))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 9 (rule_2) R->L }
% 2.32/0.89 fresh5(fresh5(theorem(or(not(not(or(p, q))), not(q))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 4 (rule_2) R->L }
% 2.32/0.89 fresh5(fresh5(fresh5(true, true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 3 (rule_3) R->L }
% 2.32/0.89 fresh5(fresh5(fresh5(fresh(true, true, q, not(not(or(p, q)))), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 7 (axiom_1_3) R->L }
% 2.32/0.89 fresh5(fresh5(fresh5(fresh(axiom(or(not(q), or(p, q))), true, q, not(not(or(p, q)))), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.89 = { by axiom 11 (rule_3) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 4 (rule_2) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(true, true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 3 (rule_3) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh(true, true, not(or(p, q)), not(or(p, q))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 7 (axiom_1_3) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh(axiom(or(not(not(or(p, q))), or(not(or(p, q)), not(or(p, q))))), true, not(or(p, q)), not(or(p, q))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 11 (rule_3) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh2(theorem(or(not(or(not(or(p, q)), not(or(p, q)))), not(or(p, q)))), true, not(or(p, q)), not(or(p, q)), or(not(or(p, q)), not(or(p, q)))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 5 (rule_1) R->L }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh2(fresh4(axiom(or(not(or(not(or(p, q)), not(or(p, q)))), not(or(p, q)))), true, or(not(or(not(or(p, q)), not(or(p, q)))), not(or(p, q)))), true, not(or(p, q)), not(or(p, q)), or(not(or(p, q)), not(or(p, q)))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 8 (axiom_1_2) }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh2(fresh4(true, true, or(not(or(not(or(p, q)), not(or(p, q)))), not(or(p, q)))), true, not(or(p, q)), not(or(p, q)), or(not(or(p, q)), not(or(p, q)))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 1 (rule_1) }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(fresh2(true, true, not(or(p, q)), not(or(p, q)), or(not(or(p, q)), not(or(p, q)))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 6 (rule_3) }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(fresh5(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, or(not(or(p, q)), not(not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q)))), true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by lemma 13 }
% 2.32/0.90 fresh5(fresh5(fresh5(fresh2(true, true, q, not(not(or(p, q))), or(p, q)), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 6 (rule_3) }
% 2.32/0.90 fresh5(fresh5(fresh5(theorem(or(not(q), not(not(or(p, q))))), true, or(not(not(or(p, q))), not(q)), or(not(q), not(not(or(p, q))))), true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by lemma 13 }
% 2.32/0.90 fresh5(fresh5(true, true, or(not(p), or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), not(q))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 4 (rule_2) }
% 2.32/0.90 fresh5(theorem(or(not(p), or(not(not(or(p, q))), not(q)))), true, or(not(not(or(p, q))), or(not(p), not(q))), or(not(p), or(not(not(or(p, q))), not(q))))
% 2.32/0.90 = { by axiom 9 (rule_2) }
% 2.32/0.90 fresh3(axiom(or(not(or(not(p), or(not(not(or(p, q))), not(q)))), or(not(not(or(p, q))), or(not(p), not(q))))), true, or(not(not(or(p, q))), or(not(p), not(q))))
% 2.32/0.90 = { by axiom 12 (axiom_1_5) }
% 2.32/0.90 fresh3(true, true, or(not(not(or(p, q))), or(not(p), not(q))))
% 2.32/0.90 = { by axiom 2 (rule_2) }
% 2.32/0.90 true
% 2.32/0.90 % SZS output end Proof
% 2.32/0.90
% 2.32/0.90 RESULT: Unsatisfiable (the axioms are contradictory).
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