TSTP Solution File: MSC005-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MSC005-1 : 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 : n023.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 09:26:58 EDT 2023
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MSC005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % 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 : n023.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 : Thu Aug 24 14:07:27 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 Take the following subset of the input axioms:
% 0.18/0.39 fof(evaluate_expression, negated_conjecture, ![Value]: ~value(xor(xor(xor(xor(truth, falsity), falsity), truth), falsity), Value)).
% 0.18/0.39 fof(false_is_false, axiom, value(falsity, falsity)).
% 0.18/0.39 fof(false_xor_false, axiom, ![X, Y]: (~value(X, falsity) | (~value(Y, falsity) | value(xor(X, Y), falsity)))).
% 0.18/0.39 fof(true_is_true, axiom, value(truth, truth)).
% 0.18/0.39 fof(true_xor_false, axiom, ![X2, Y2]: (~value(X2, truth) | (~value(Y2, falsity) | value(xor(X2, Y2), truth)))).
% 0.18/0.39 fof(true_xor_true, axiom, ![X2, Y2]: (~value(X2, truth) | (~value(Y2, truth) | value(xor(X2, Y2), falsity)))).
% 0.18/0.39
% 0.18/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.39 fresh(y, y, x1...xn) = u
% 0.18/0.39 C => fresh(s, t, x1...xn) = v
% 0.18/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.39 variables of u and v.
% 0.18/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.39 input problem has no model of domain size 1).
% 0.18/0.39
% 0.18/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.39
% 0.18/0.39 Axiom 1 (false_is_false): value(falsity, falsity) = true2.
% 0.18/0.39 Axiom 2 (true_is_true): value(truth, truth) = true2.
% 0.18/0.39 Axiom 3 (true_xor_true): fresh(X, X, Y, Z) = true2.
% 0.18/0.39 Axiom 4 (false_xor_false): fresh8(X, X, Y, Z) = true2.
% 0.18/0.39 Axiom 5 (false_xor_false): fresh7(X, X, Y, Z) = value(xor(Y, Z), falsity).
% 0.18/0.39 Axiom 6 (true_xor_false): fresh4(X, X, Y, Z) = value(xor(Y, Z), truth).
% 0.18/0.39 Axiom 7 (true_xor_false): fresh3(X, X, Y, Z) = true2.
% 0.18/0.39 Axiom 8 (true_xor_true): fresh2(X, X, Y, Z) = value(xor(Y, Z), falsity).
% 0.18/0.39 Axiom 9 (false_xor_false): fresh7(value(X, falsity), true2, Y, X) = fresh8(value(Y, falsity), true2, Y, X).
% 0.18/0.39 Axiom 10 (true_xor_false): fresh4(value(X, falsity), true2, Y, X) = fresh3(value(Y, truth), true2, Y, X).
% 0.18/0.39 Axiom 11 (true_xor_true): fresh2(value(X, truth), true2, Y, X) = fresh(value(Y, truth), true2, Y, X).
% 0.18/0.39
% 0.18/0.39 Goal 1 (evaluate_expression): value(xor(xor(xor(xor(truth, falsity), falsity), truth), falsity), X) = true2.
% 0.18/0.39 The goal is true when:
% 0.18/0.39 X = falsity
% 0.18/0.39
% 0.18/0.39 Proof:
% 0.18/0.39 value(xor(xor(xor(xor(truth, falsity), falsity), truth), falsity), falsity)
% 0.18/0.39 = { by axiom 5 (false_xor_false) R->L }
% 0.18/0.39 fresh7(true2, true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 1 (false_is_false) R->L }
% 0.18/0.39 fresh7(value(falsity, falsity), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 9 (false_xor_false) }
% 0.18/0.39 fresh8(value(xor(xor(xor(truth, falsity), falsity), truth), falsity), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 8 (true_xor_true) R->L }
% 0.18/0.39 fresh8(fresh2(true2, true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 2 (true_is_true) R->L }
% 0.18/0.39 fresh8(fresh2(value(truth, truth), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 11 (true_xor_true) }
% 0.18/0.39 fresh8(fresh(value(xor(xor(truth, falsity), falsity), truth), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 6 (true_xor_false) R->L }
% 0.18/0.39 fresh8(fresh(fresh4(true2, true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 1 (false_is_false) R->L }
% 0.18/0.39 fresh8(fresh(fresh4(value(falsity, falsity), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 10 (true_xor_false) }
% 0.18/0.39 fresh8(fresh(fresh3(value(xor(truth, falsity), truth), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 6 (true_xor_false) R->L }
% 0.18/0.39 fresh8(fresh(fresh3(fresh4(true2, true2, truth, falsity), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 1 (false_is_false) R->L }
% 0.18/0.39 fresh8(fresh(fresh3(fresh4(value(falsity, falsity), true2, truth, falsity), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 10 (true_xor_false) }
% 0.18/0.39 fresh8(fresh(fresh3(fresh3(value(truth, truth), true2, truth, falsity), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 2 (true_is_true) }
% 0.18/0.39 fresh8(fresh(fresh3(fresh3(true2, true2, truth, falsity), true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 7 (true_xor_false) }
% 0.18/0.39 fresh8(fresh(fresh3(true2, true2, xor(truth, falsity), falsity), true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 7 (true_xor_false) }
% 0.18/0.39 fresh8(fresh(true2, true2, xor(xor(truth, falsity), falsity), truth), true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 3 (true_xor_true) }
% 0.18/0.39 fresh8(true2, true2, xor(xor(xor(truth, falsity), falsity), truth), falsity)
% 0.18/0.39 = { by axiom 4 (false_xor_false) }
% 0.18/0.39 true2
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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