TSTP Solution File: HWV001-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HWV001-1 : 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 : n028.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 02:31:29 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV001-1 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 14:43:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.57
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 Take the following subset of the input axioms:
% 0.19/0.64 fof(and_associativity, axiom, ![X, Y, Z]: and(X, and(Y, Z))=and(and(X, Y), Z)).
% 0.19/0.64 fof(and_commutativity, axiom, ![X2, Y2]: and(X2, Y2)=and(Y2, X2)).
% 0.19/0.64 fof(and_not_simplification1, axiom, ![X2]: and(X2, not(X2))=n0).
% 0.19/0.64 fof(and_not_simplification3, axiom, ![X2, Y2]: and(and(X2, Y2), not(X2))=n0).
% 0.19/0.64 fof(and_or_canonicalization, axiom, ![X2, Y2, Z2]: and(or(X2, Y2), Z2)=or(and(X2, Z2), and(Y2, Z2))).
% 0.19/0.64 fof(and_or_not_simplification1, axiom, ![X2, Y2]: or(and(X2, Y2), and(X2, not(Y2)))=X2).
% 0.19/0.64 fof(and_or_not_simplification2, axiom, ![X2, Y2]: or(and(X2, Y2), and(Y2, not(X2)))=Y2).
% 0.19/0.64 fof(and_simplification1, axiom, ![X2]: and(X2, X2)=X2).
% 0.19/0.64 fof(and_simplification2, axiom, ![X2, Y2]: and(and(X2, Y2), Y2)=and(X2, Y2)).
% 0.19/0.64 fof(and_simplification3, axiom, ![X2, Y2]: and(and(X2, Y2), X2)=and(X2, Y2)).
% 0.19/0.64 fof(circuit_description, negated_conjecture, circuit(input(i1, i2), output(a1, a2))).
% 0.19/0.64 fof(constructor1, negated_conjecture, a1=and(b1, b3)).
% 0.19/0.64 fof(constructor10, negated_conjecture, d2=not(e2)).
% 0.19/0.64 fof(constructor11, negated_conjecture, e1=or(f1, f3)).
% 0.19/0.64 fof(constructor12, negated_conjecture, e2=or(f2, f3)).
% 0.19/0.64 fof(constructor13, negated_conjecture, f1=not(i1)).
% 0.19/0.64 fof(constructor14, negated_conjecture, f2=not(i2)).
% 0.19/0.64 fof(constructor15, negated_conjecture, f3=and(i1, i2)).
% 0.19/0.64 fof(constructor2, negated_conjecture, a2=and(b2, b3)).
% 0.19/0.64 fof(constructor3, negated_conjecture, b1=not(d1)).
% 0.19/0.64 fof(constructor4, negated_conjecture, b2=not(d2)).
% 0.19/0.64 fof(constructor5, negated_conjecture, b3=or(c1, c2)).
% 0.19/0.64 fof(constructor6, negated_conjecture, c1=or(d1, d3)).
% 0.19/0.64 fof(constructor7, negated_conjecture, c2=or(d2, d3)).
% 0.19/0.64 fof(constructor8, negated_conjecture, d3=f3).
% 0.19/0.64 fof(constructor9, negated_conjecture, d1=not(e1)).
% 0.19/0.64 fof(not_canonicalization1, axiom, ![X2, Y2]: not(and(X2, Y2))=or(not(X2), not(Y2))).
% 0.19/0.64 fof(not_canonicalization2, axiom, ![X2, Y2]: not(or(X2, Y2))=and(not(X2), not(Y2))).
% 0.19/0.64 fof(not_definition2, axiom, not(n1)=n0).
% 0.19/0.64 fof(not_simplification, axiom, ![X2]: not(not(X2))=X2).
% 0.19/0.64 fof(or_associativity, axiom, ![X2, Y2, Z2]: or(X2, or(Y2, Z2))=or(or(X2, Y2), Z2)).
% 0.19/0.64 fof(or_commutativity, axiom, ![X2, Y2]: or(X2, Y2)=or(Y2, X2)).
% 0.19/0.64 fof(or_definition1, axiom, ![X2]: or(X2, n0)=X2).
% 0.19/0.64 fof(or_definition2, axiom, ![X2]: or(X2, n1)=n1).
% 0.19/0.64 fof(or_not_simplification3, axiom, ![X2, Y2]: or(or(X2, Y2), not(X2))=n1).
% 0.19/0.64 fof(or_simplification2, axiom, ![X2, Y2]: or(or(X2, Y2), Y2)=or(X2, Y2)).
% 0.19/0.64 fof(or_simplification3, axiom, ![X2, Y2]: or(or(X2, Y2), X2)=or(X2, Y2)).
% 0.19/0.64 fof(prove_interchange, negated_conjecture, ~circuit(input(i1, i2), output(i2, i1))).
% 0.19/0.64
% 0.19/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.64 fresh(y, y, x1...xn) = u
% 0.19/0.64 C => fresh(s, t, x1...xn) = v
% 0.19/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.64 variables of u and v.
% 0.19/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.64 input problem has no model of domain size 1).
% 0.19/0.64
% 0.19/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.64
% 0.19/0.64 Axiom 1 (constructor8): d3 = f3.
% 0.19/0.64 Axiom 2 (constructor13): f1 = not(i1).
% 0.19/0.64 Axiom 3 (constructor14): f2 = not(i2).
% 0.19/0.64 Axiom 4 (not_definition2): not(n1) = n0.
% 0.19/0.64 Axiom 5 (constructor3): b1 = not(d1).
% 0.19/0.64 Axiom 6 (constructor4): b2 = not(d2).
% 0.19/0.64 Axiom 7 (constructor9): d1 = not(e1).
% 0.19/0.64 Axiom 8 (constructor10): d2 = not(e2).
% 0.19/0.64 Axiom 9 (and_simplification1): and(X, X) = X.
% 0.19/0.64 Axiom 10 (and_commutativity): and(X, Y) = and(Y, X).
% 0.19/0.64 Axiom 11 (constructor15): f3 = and(i1, i2).
% 0.19/0.64 Axiom 12 (constructor1): a1 = and(b1, b3).
% 0.19/0.64 Axiom 13 (constructor2): a2 = and(b2, b3).
% 0.19/0.64 Axiom 14 (or_commutativity): or(X, Y) = or(Y, X).
% 0.19/0.64 Axiom 15 (or_definition1): or(X, n0) = X.
% 0.19/0.64 Axiom 16 (or_definition2): or(X, n1) = n1.
% 0.19/0.64 Axiom 17 (constructor6): c1 = or(d1, d3).
% 0.19/0.64 Axiom 18 (constructor7): c2 = or(d2, d3).
% 0.19/0.64 Axiom 19 (constructor5): b3 = or(c1, c2).
% 0.19/0.64 Axiom 20 (constructor11): e1 = or(f1, f3).
% 0.19/0.64 Axiom 21 (constructor12): e2 = or(f2, f3).
% 0.19/0.64 Axiom 22 (not_simplification): not(not(X)) = X.
% 0.19/0.64 Axiom 23 (and_not_simplification1): and(X, not(X)) = n0.
% 0.19/0.64 Axiom 24 (not_canonicalization2): not(or(X, Y)) = and(not(X), not(Y)).
% 0.19/0.64 Axiom 25 (and_simplification3): and(and(X, Y), X) = and(X, Y).
% 0.19/0.64 Axiom 26 (and_simplification2): and(and(X, Y), Y) = and(X, Y).
% 0.19/0.64 Axiom 27 (and_associativity): and(X, and(Y, Z)) = and(and(X, Y), Z).
% 0.19/0.64 Axiom 28 (not_canonicalization1): not(and(X, Y)) = or(not(X), not(Y)).
% 0.19/0.64 Axiom 29 (or_simplification3): or(or(X, Y), X) = or(X, Y).
% 0.19/0.64 Axiom 30 (or_simplification2): or(or(X, Y), Y) = or(X, Y).
% 0.19/0.64 Axiom 31 (or_associativity): or(X, or(Y, Z)) = or(or(X, Y), Z).
% 0.19/0.64 Axiom 32 (and_not_simplification3): and(and(X, Y), not(X)) = n0.
% 0.19/0.64 Axiom 33 (or_not_simplification3): or(or(X, Y), not(X)) = n1.
% 0.19/0.64 Axiom 34 (and_or_canonicalization): and(or(X, Y), Z) = or(and(X, Z), and(Y, Z)).
% 0.19/0.64 Axiom 35 (circuit_description): circuit(input(i1, i2), output(a1, a2)) = true.
% 0.19/0.64 Axiom 36 (and_or_not_simplification1): or(and(X, Y), and(X, not(Y))) = X.
% 0.19/0.64 Axiom 37 (and_or_not_simplification2): or(and(X, Y), and(Y, not(X))) = Y.
% 0.19/0.64
% 0.19/0.64 Lemma 38: and(b3, b2) = a2.
% 0.19/0.64 Proof:
% 0.19/0.64 and(b3, b2)
% 0.19/0.64 = { by axiom 10 (and_commutativity) R->L }
% 0.19/0.64 and(b2, b3)
% 0.19/0.64 = { by axiom 13 (constructor2) R->L }
% 0.19/0.64 a2
% 0.19/0.64
% 0.19/0.64 Lemma 39: and(b3, and(X, b2)) = and(X, a2).
% 0.19/0.64 Proof:
% 0.19/0.64 and(b3, and(X, b2))
% 0.19/0.64 = { by axiom 10 (and_commutativity) R->L }
% 0.19/0.64 and(b3, and(b2, X))
% 0.19/0.64 = { by axiom 27 (and_associativity) }
% 0.19/0.64 and(and(b3, b2), X)
% 0.19/0.64 = { by lemma 38 }
% 0.19/0.64 and(a2, X)
% 0.19/0.64 = { by axiom 10 (and_commutativity) }
% 0.19/0.64 and(X, a2)
% 0.19/0.64
% 0.19/0.64 Lemma 40: or(f3, d2) = c2.
% 0.19/0.64 Proof:
% 0.19/0.64 or(f3, d2)
% 0.19/0.64 = { by axiom 14 (or_commutativity) R->L }
% 0.19/0.64 or(d2, f3)
% 0.19/0.64 = { by axiom 1 (constructor8) R->L }
% 0.19/0.64 or(d2, d3)
% 0.19/0.64 = { by axiom 18 (constructor7) R->L }
% 0.19/0.64 c2
% 0.19/0.64
% 0.19/0.64 Lemma 41: or(f3, f2) = e2.
% 0.19/0.64 Proof:
% 0.19/0.64 or(f3, f2)
% 0.19/0.64 = { by axiom 14 (or_commutativity) R->L }
% 0.19/0.64 or(f2, f3)
% 0.19/0.64 = { by axiom 21 (constructor12) R->L }
% 2.14/0.64 e2
% 2.14/0.64
% 2.14/0.64 Lemma 42: not(f2) = i2.
% 2.14/0.64 Proof:
% 2.14/0.64 not(f2)
% 2.14/0.64 = { by axiom 3 (constructor14) }
% 2.14/0.64 not(not(i2))
% 2.14/0.64 = { by axiom 22 (not_simplification) }
% 2.14/0.64 i2
% 2.14/0.64
% 2.14/0.64 Lemma 43: c2 = i2.
% 2.14/0.64 Proof:
% 2.14/0.64 c2
% 2.14/0.64 = { by lemma 40 R->L }
% 2.14/0.64 or(f3, d2)
% 2.14/0.64 = { by axiom 11 (constructor15) }
% 2.14/0.64 or(and(i1, i2), d2)
% 2.14/0.64 = { by axiom 26 (and_simplification2) R->L }
% 2.14/0.64 or(and(and(i1, i2), i2), d2)
% 2.14/0.64 = { by axiom 10 (and_commutativity) }
% 2.14/0.64 or(and(i2, and(i1, i2)), d2)
% 2.14/0.64 = { by axiom 11 (constructor15) R->L }
% 2.14/0.64 or(and(i2, f3), d2)
% 2.14/0.64 = { by axiom 8 (constructor10) }
% 2.14/0.64 or(and(i2, f3), not(e2))
% 2.14/0.64 = { by lemma 41 R->L }
% 2.14/0.64 or(and(i2, f3), not(or(f3, f2)))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(and(i2, f3), not(or(f2, f3)))
% 2.14/0.64 = { by axiom 24 (not_canonicalization2) }
% 2.14/0.64 or(and(i2, f3), and(not(f2), not(f3)))
% 2.14/0.64 = { by lemma 42 }
% 2.14/0.64 or(and(i2, f3), and(i2, not(f3)))
% 2.14/0.64 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.64 i2
% 2.14/0.64
% 2.14/0.64 Lemma 44: or(f3, d1) = c1.
% 2.14/0.64 Proof:
% 2.14/0.64 or(f3, d1)
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(d1, f3)
% 2.14/0.64 = { by axiom 1 (constructor8) R->L }
% 2.14/0.64 or(d1, d3)
% 2.14/0.64 = { by axiom 17 (constructor6) R->L }
% 2.14/0.64 c1
% 2.14/0.64
% 2.14/0.64 Lemma 45: and(i1, not(f3)) = d1.
% 2.14/0.64 Proof:
% 2.14/0.64 and(i1, not(f3))
% 2.14/0.64 = { by axiom 22 (not_simplification) R->L }
% 2.14/0.64 and(not(not(i1)), not(f3))
% 2.14/0.64 = { by axiom 2 (constructor13) R->L }
% 2.14/0.64 and(not(f1), not(f3))
% 2.14/0.64 = { by axiom 24 (not_canonicalization2) R->L }
% 2.14/0.64 not(or(f1, f3))
% 2.14/0.64 = { by axiom 20 (constructor11) R->L }
% 2.14/0.64 not(e1)
% 2.14/0.64 = { by axiom 7 (constructor9) R->L }
% 2.14/0.64 d1
% 2.14/0.64
% 2.14/0.64 Lemma 46: c1 = i1.
% 2.14/0.64 Proof:
% 2.14/0.64 c1
% 2.14/0.64 = { by lemma 44 R->L }
% 2.14/0.64 or(f3, d1)
% 2.14/0.64 = { by axiom 11 (constructor15) }
% 2.14/0.64 or(and(i1, i2), d1)
% 2.14/0.64 = { by axiom 25 (and_simplification3) R->L }
% 2.14/0.64 or(and(and(i1, i2), i1), d1)
% 2.14/0.64 = { by axiom 10 (and_commutativity) }
% 2.14/0.64 or(and(i1, and(i1, i2)), d1)
% 2.14/0.64 = { by axiom 11 (constructor15) R->L }
% 2.14/0.64 or(and(i1, f3), d1)
% 2.14/0.64 = { by lemma 45 R->L }
% 2.14/0.64 or(and(i1, f3), and(i1, not(f3)))
% 2.14/0.64 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.64 i1
% 2.14/0.64
% 2.14/0.64 Lemma 47: or(i1, i2) = b3.
% 2.14/0.64 Proof:
% 2.14/0.64 or(i1, i2)
% 2.14/0.64 = { by lemma 46 R->L }
% 2.14/0.64 or(c1, i2)
% 2.14/0.64 = { by lemma 43 R->L }
% 2.14/0.64 or(c1, c2)
% 2.14/0.64 = { by axiom 19 (constructor5) R->L }
% 2.14/0.64 b3
% 2.14/0.64
% 2.14/0.64 Lemma 48: or(n0, X) = X.
% 2.14/0.64 Proof:
% 2.14/0.64 or(n0, X)
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(X, n0)
% 2.14/0.64 = { by axiom 15 (or_definition1) }
% 2.14/0.64 X
% 2.14/0.64
% 2.14/0.64 Lemma 49: and(a2, not(f3)) = and(i1, f2).
% 2.14/0.64 Proof:
% 2.14/0.64 and(a2, not(f3))
% 2.14/0.64 = { by axiom 10 (and_commutativity) R->L }
% 2.14/0.64 and(not(f3), a2)
% 2.14/0.64 = { by lemma 39 R->L }
% 2.14/0.64 and(b3, and(not(f3), b2))
% 2.14/0.64 = { by axiom 10 (and_commutativity) }
% 2.14/0.64 and(b3, and(b2, not(f3)))
% 2.14/0.64 = { by axiom 6 (constructor4) }
% 2.14/0.64 and(b3, and(not(d2), not(f3)))
% 2.14/0.64 = { by axiom 24 (not_canonicalization2) R->L }
% 2.14/0.64 and(b3, not(or(d2, f3)))
% 2.14/0.64 = { by axiom 14 (or_commutativity) }
% 2.14/0.64 and(b3, not(or(f3, d2)))
% 2.14/0.64 = { by lemma 40 }
% 2.14/0.64 and(b3, not(c2))
% 2.14/0.64 = { by lemma 43 }
% 2.14/0.64 and(b3, not(i2))
% 2.14/0.64 = { by axiom 3 (constructor14) R->L }
% 2.14/0.64 and(b3, f2)
% 2.14/0.64 = { by axiom 10 (and_commutativity) R->L }
% 2.14/0.64 and(f2, b3)
% 2.14/0.64 = { by lemma 47 R->L }
% 2.14/0.64 and(f2, or(i1, i2))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 and(f2, or(i2, i1))
% 2.14/0.64 = { by axiom 10 (and_commutativity) R->L }
% 2.14/0.64 and(or(i2, i1), f2)
% 2.14/0.64 = { by axiom 34 (and_or_canonicalization) }
% 2.14/0.64 or(and(i2, f2), and(i1, f2))
% 2.14/0.64 = { by axiom 3 (constructor14) }
% 2.14/0.64 or(and(i2, not(i2)), and(i1, f2))
% 2.14/0.64 = { by axiom 23 (and_not_simplification1) }
% 2.14/0.64 or(n0, and(i1, f2))
% 2.14/0.64 = { by lemma 48 }
% 2.14/0.64 and(i1, f2)
% 2.14/0.64
% 2.14/0.64 Lemma 50: e2 = b2.
% 2.14/0.64 Proof:
% 2.14/0.64 e2
% 2.14/0.64 = { by axiom 22 (not_simplification) R->L }
% 2.14/0.64 not(not(e2))
% 2.14/0.64 = { by axiom 8 (constructor10) R->L }
% 2.14/0.64 not(d2)
% 2.14/0.64 = { by axiom 6 (constructor4) R->L }
% 2.14/0.64 b2
% 2.14/0.64
% 2.14/0.64 Lemma 51: not(or(X, b2)) = and(d2, not(X)).
% 2.14/0.64 Proof:
% 2.14/0.64 not(or(X, b2))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 not(or(b2, X))
% 2.14/0.64 = { by lemma 50 R->L }
% 2.14/0.64 not(or(e2, X))
% 2.14/0.64 = { by axiom 24 (not_canonicalization2) }
% 2.14/0.64 and(not(e2), not(X))
% 2.14/0.64 = { by axiom 8 (constructor10) R->L }
% 2.14/0.64 and(d2, not(X))
% 2.14/0.64
% 2.14/0.64 Lemma 52: or(X, or(X, Y)) = or(X, Y).
% 2.14/0.64 Proof:
% 2.14/0.64 or(X, or(X, Y))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(or(X, Y), X)
% 2.14/0.64 = { by axiom 29 (or_simplification3) }
% 2.14/0.64 or(X, Y)
% 2.14/0.64
% 2.14/0.64 Lemma 53: or(f3, or(X, d2)) = or(X, i2).
% 2.14/0.64 Proof:
% 2.14/0.64 or(f3, or(X, d2))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(f3, or(d2, X))
% 2.14/0.64 = { by axiom 31 (or_associativity) }
% 2.14/0.64 or(or(f3, d2), X)
% 2.14/0.64 = { by lemma 40 }
% 2.14/0.64 or(c2, X)
% 2.14/0.64 = { by lemma 43 }
% 2.14/0.64 or(i2, X)
% 2.14/0.64 = { by axiom 14 (or_commutativity) }
% 2.14/0.64 or(X, i2)
% 2.14/0.64
% 2.14/0.64 Lemma 54: and(X, or(X, Y)) = X.
% 2.14/0.64 Proof:
% 2.14/0.64 and(X, or(X, Y))
% 2.14/0.64 = { by axiom 10 (and_commutativity) R->L }
% 2.14/0.64 and(or(X, Y), X)
% 2.14/0.64 = { by axiom 34 (and_or_canonicalization) }
% 2.14/0.64 or(and(X, X), and(Y, X))
% 2.14/0.64 = { by axiom 9 (and_simplification1) }
% 2.14/0.64 or(X, and(Y, X))
% 2.14/0.64 = { by axiom 10 (and_commutativity) R->L }
% 2.14/0.64 or(X, and(X, Y))
% 2.14/0.64 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.64 or(and(X, Y), X)
% 2.14/0.64 = { by axiom 36 (and_or_not_simplification1) R->L }
% 2.14/0.64 or(and(X, Y), or(and(X, Y), and(X, not(Y))))
% 2.14/0.64 = { by lemma 52 }
% 2.14/0.64 or(and(X, Y), and(X, not(Y)))
% 2.14/0.64 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.64 X
% 2.14/0.64
% 2.14/0.64 Lemma 55: a2 = i1.
% 2.14/0.64 Proof:
% 2.14/0.64 a2
% 2.14/0.64 = { by axiom 37 (and_or_not_simplification2) R->L }
% 2.14/0.64 or(and(f3, a2), and(a2, not(f3)))
% 2.14/0.64 = { by lemma 49 }
% 2.14/0.64 or(and(f3, a2), and(i1, f2))
% 2.14/0.64 = { by lemma 39 R->L }
% 2.14/0.64 or(and(b3, and(f3, b2)), and(i1, f2))
% 2.14/0.64 = { by axiom 6 (constructor4) }
% 2.14/0.64 or(and(b3, and(f3, not(d2))), and(i1, f2))
% 2.14/0.64 = { by lemma 48 R->L }
% 2.14/0.64 or(and(b3, or(n0, and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by axiom 32 (and_not_simplification3) R->L }
% 2.14/0.64 or(and(b3, or(and(and(f3, d2), not(f3)), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by axiom 27 (and_associativity) R->L }
% 2.14/0.64 or(and(b3, or(and(f3, and(d2, not(f3))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 51 R->L }
% 2.14/0.64 or(and(b3, or(and(f3, not(or(f3, b2))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 50 R->L }
% 2.14/0.64 or(and(b3, or(and(f3, not(or(f3, e2))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 41 R->L }
% 2.14/0.64 or(and(b3, or(and(f3, not(or(f3, or(f3, f2)))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 52 }
% 2.14/0.64 or(and(b3, or(and(f3, not(or(f3, f2))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 41 }
% 2.14/0.64 or(and(b3, or(and(f3, not(e2)), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by lemma 50 }
% 2.14/0.64 or(and(b3, or(and(f3, not(b2)), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.64 = { by axiom 6 (constructor4) }
% 2.14/0.65 or(and(b3, or(and(f3, not(not(d2))), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.65 = { by axiom 22 (not_simplification) }
% 2.14/0.65 or(and(b3, or(and(f3, d2), and(f3, not(d2)))), and(i1, f2))
% 2.14/0.65 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.65 or(and(b3, f3), and(i1, f2))
% 2.14/0.65 = { by axiom 10 (and_commutativity) }
% 2.14/0.65 or(and(f3, b3), and(i1, f2))
% 2.14/0.65 = { by lemma 47 R->L }
% 2.14/0.65 or(and(f3, or(i1, i2)), and(i1, f2))
% 2.14/0.65 = { by lemma 53 R->L }
% 2.14/0.65 or(and(f3, or(f3, or(i1, d2))), and(i1, f2))
% 2.14/0.65 = { by lemma 54 }
% 2.14/0.65 or(f3, and(i1, f2))
% 2.14/0.65 = { by axiom 3 (constructor14) }
% 2.14/0.65 or(f3, and(i1, not(i2)))
% 2.14/0.65 = { by axiom 11 (constructor15) }
% 2.14/0.65 or(and(i1, i2), and(i1, not(i2)))
% 2.14/0.65 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.65 i1
% 2.14/0.65
% 2.14/0.65 Goal 1 (prove_interchange): circuit(input(i1, i2), output(i2, i1)) = true.
% 2.14/0.65 Proof:
% 2.14/0.65 circuit(input(i1, i2), output(i2, i1))
% 2.14/0.65 = { by lemma 55 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(i2, a2))
% 2.14/0.65 = { by lemma 54 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, or(i2, f1)), a2))
% 2.14/0.65 = { by axiom 2 (constructor13) }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, or(i2, not(i1))), a2))
% 2.14/0.65 = { by lemma 42 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, or(not(f2), not(i1))), a2))
% 2.14/0.65 = { by axiom 28 (not_canonicalization1) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, not(and(f2, i1))), a2))
% 2.14/0.65 = { by axiom 10 (and_commutativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, not(and(i1, f2))), a2))
% 2.14/0.65 = { by lemma 49 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, not(and(a2, not(f3)))), a2))
% 2.14/0.65 = { by lemma 55 }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, not(and(i1, not(f3)))), a2))
% 2.14/0.65 = { by lemma 45 }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, not(d1)), a2))
% 2.14/0.65 = { by axiom 5 (constructor3) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(i2, b1), a2))
% 2.14/0.65 = { by lemma 48 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(or(n0, and(i2, b1)), a2))
% 2.14/0.65 = { by axiom 23 (and_not_simplification1) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(or(and(d1, not(d1)), and(i2, b1)), a2))
% 2.14/0.65 = { by axiom 5 (constructor3) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(or(and(d1, b1), and(i2, b1)), a2))
% 2.14/0.65 = { by axiom 34 (and_or_canonicalization) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(or(d1, i2), b1), a2))
% 2.14/0.65 = { by axiom 10 (and_commutativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(d1, i2)), a2))
% 2.14/0.65 = { by lemma 53 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(f3, or(d1, d2))), a2))
% 2.14/0.65 = { by axiom 31 (or_associativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(f3, d1), d2)), a2))
% 2.14/0.65 = { by lemma 44 }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(c1, d2)), a2))
% 2.14/0.65 = { by lemma 46 }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(i1, d2)), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(d2, i1)), a2))
% 2.14/0.65 = { by lemma 55 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(d2, a2)), a2))
% 2.14/0.65 = { by lemma 38 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(d2, and(b3, b2))), a2))
% 2.14/0.65 = { by axiom 6 (constructor4) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(d2, and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 36 (and_or_not_simplification1) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(and(d2, not(b3)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by lemma 51 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(b3, b2)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(b2, b3)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by lemma 50 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(e2, b3)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by lemma 41 R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(or(f3, f2), b3)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 31 (or_associativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(f2, b3))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(b3, f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 19 (constructor5) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(c1, c2), f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 30 (or_simplification2) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(or(c1, c2), c2), f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(c2, or(c1, c2)), f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 19 (constructor5) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(c2, b3), f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(b3, c2), f2))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 31 (or_associativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(b3, or(c2, f2)))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by lemma 43 }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(b3, or(i2, f2)))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(i2, f2), b3))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 31 (or_associativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(i2, or(f2, b3)))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 14 (or_commutativity) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(i2, or(b3, f2)))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 3 (constructor14) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(i2, or(b3, not(i2))))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 31 (or_associativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, or(or(i2, b3), not(i2)))), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 33 (or_not_simplification3) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(or(f3, n1)), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 16 (or_definition2) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(not(n1), and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 4 (not_definition2) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(or(n0, and(d2, not(not(b3)))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by lemma 48 }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(and(d2, not(not(b3))), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 22 (not_simplification) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(and(d2, b3), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 10 (and_commutativity) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, or(and(b3, d2), and(b3, not(d2)))), a2))
% 2.14/0.65 = { by axiom 36 (and_or_not_simplification1) }
% 2.14/0.65 circuit(input(i1, i2), output(and(b1, b3), a2))
% 2.14/0.65 = { by axiom 12 (constructor1) R->L }
% 2.14/0.65 circuit(input(i1, i2), output(a1, a2))
% 2.14/0.65 = { by axiom 35 (circuit_description) }
% 2.14/0.65 true
% 2.14/0.65 % SZS output end Proof
% 2.14/0.65
% 2.14/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------