TSTP Solution File: LCL215-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL215-3 : TPTP v8.1.2. Released v2.3.0.
% 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 : n008.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 08:18:03 EDT 2023
% Result : Unsatisfiable 55.12s 7.55s
% Output : Proof 55.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL215-3 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n008.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 : Fri Aug 25 06:18:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 55.12/7.55 Command-line arguments: --flatten
% 55.12/7.55
% 55.12/7.55 % SZS status Unsatisfiable
% 55.12/7.55
% 55.12/7.61 % SZS output start Proof
% 55.12/7.61 Take the following subset of the input axioms:
% 55.12/7.61 fof(axiom_1_2, axiom, ![A]: axiom(implies(or(A, A), A))).
% 55.12/7.61 fof(axiom_1_3, axiom, ![B, A2]: axiom(implies(A2, or(B, A2)))).
% 55.12/7.61 fof(axiom_1_4, axiom, ![A2, B2]: axiom(implies(or(A2, B2), or(B2, A2)))).
% 55.12/7.61 fof(axiom_1_5, axiom, ![C, A2, B2]: axiom(implies(or(A2, or(B2, C)), or(B2, or(A2, C))))).
% 55.12/7.61 fof(axiom_1_6, axiom, ![A2, B2, C2]: axiom(implies(implies(A2, B2), implies(or(C2, A2), or(C2, B2))))).
% 55.12/7.61 fof(implies_definition, axiom, ![X, Y]: implies(X, Y)=or(not(X), Y)).
% 55.12/7.61 fof(prove_this, negated_conjecture, ~theorem(implies(implies(p, q), implies(or(p, q), q)))).
% 55.12/7.61 fof(rule_1, axiom, ![X2]: (theorem(X2) | ~axiom(X2))).
% 55.12/7.61 fof(rule_2, axiom, ![X2, Y2]: (theorem(X2) | (~theorem(implies(Y2, X2)) | ~theorem(Y2)))).
% 55.12/7.61
% 55.12/7.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 55.12/7.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 55.12/7.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 55.12/7.61 fresh(y, y, x1...xn) = u
% 55.12/7.61 C => fresh(s, t, x1...xn) = v
% 55.12/7.61 where fresh is a fresh function symbol and x1..xn are the free
% 55.12/7.61 variables of u and v.
% 55.12/7.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 55.12/7.61 input problem has no model of domain size 1).
% 55.12/7.61
% 55.12/7.61 The encoding turns the above axioms into the following unit equations and goals:
% 55.12/7.61
% 55.12/7.61 Axiom 1 (rule_2): fresh(X, X, Y) = true.
% 55.12/7.61 Axiom 2 (rule_1): fresh2(X, X, Y) = true.
% 55.12/7.61 Axiom 3 (implies_definition): implies(X, Y) = or(not(X), Y).
% 55.12/7.61 Axiom 4 (rule_2): fresh3(X, X, Y, Z) = theorem(Y).
% 55.12/7.61 Axiom 5 (rule_1): fresh2(axiom(X), true, X) = theorem(X).
% 55.12/7.61 Axiom 6 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 55.12/7.61 Axiom 7 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 55.12/7.61 Axiom 8 (rule_2): fresh3(theorem(implies(X, Y)), true, Y, X) = fresh(theorem(X), true, Y).
% 55.12/7.61 Axiom 9 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 55.12/7.61 Axiom 10 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 55.12/7.61 Axiom 11 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 55.12/7.61
% 55.12/7.61 Lemma 12: theorem(implies(X, or(Y, X))) = true.
% 55.12/7.61 Proof:
% 55.12/7.61 theorem(implies(X, or(Y, X)))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh2(axiom(implies(X, or(Y, X))), true, implies(X, or(Y, X)))
% 55.12/7.61 = { by axiom 6 (axiom_1_3) }
% 55.12/7.61 fresh2(true, true, implies(X, or(Y, X)))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 true
% 55.12/7.61
% 55.12/7.61 Lemma 13: theorem(implies(X, implies(Y, X))) = true.
% 55.12/7.61 Proof:
% 55.12/7.61 theorem(implies(X, implies(Y, X)))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh2(axiom(implies(X, implies(Y, X))), true, implies(X, implies(Y, X)))
% 55.12/7.61 = { by axiom 3 (implies_definition) }
% 55.12/7.61 fresh2(axiom(implies(X, or(not(Y), X))), true, implies(X, implies(Y, X)))
% 55.12/7.61 = { by axiom 6 (axiom_1_3) }
% 55.12/7.61 fresh2(true, true, implies(X, implies(Y, X)))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 true
% 55.12/7.61
% 55.12/7.61 Lemma 14: theorem(implies(or(X, X), X)) = true.
% 55.12/7.61 Proof:
% 55.12/7.61 theorem(implies(or(X, X), X))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh2(axiom(implies(or(X, X), X)), true, implies(or(X, X), X))
% 55.12/7.61 = { by axiom 7 (axiom_1_2) }
% 55.12/7.61 fresh2(true, true, implies(or(X, X), X))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 true
% 55.12/7.61
% 55.12/7.61 Lemma 15: fresh(theorem(or(X, X)), true, X) = theorem(X).
% 55.12/7.61 Proof:
% 55.12/7.61 fresh(theorem(or(X, X)), true, X)
% 55.12/7.61 = { by axiom 8 (rule_2) R->L }
% 55.12/7.61 fresh3(theorem(implies(or(X, X), X)), true, X, or(X, X))
% 55.12/7.61 = { by lemma 14 }
% 55.12/7.61 fresh3(true, true, X, or(X, X))
% 55.12/7.61 = { by axiom 4 (rule_2) }
% 55.12/7.61 theorem(X)
% 55.12/7.61
% 55.12/7.61 Lemma 16: theorem(implies(or(X, Y), or(Y, X))) = true.
% 55.12/7.61 Proof:
% 55.12/7.61 theorem(implies(or(X, Y), or(Y, X)))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh2(axiom(implies(or(X, Y), or(Y, X))), true, implies(or(X, Y), or(Y, X)))
% 55.12/7.61 = { by axiom 9 (axiom_1_4) }
% 55.12/7.61 fresh2(true, true, implies(or(X, Y), or(Y, X)))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 true
% 55.12/7.61
% 55.12/7.61 Lemma 17: fresh(theorem(or(X, Y)), true, or(Y, X)) = theorem(or(Y, X)).
% 55.12/7.61 Proof:
% 55.12/7.61 fresh(theorem(or(X, Y)), true, or(Y, X))
% 55.12/7.61 = { by axiom 8 (rule_2) R->L }
% 55.12/7.61 fresh3(theorem(implies(or(X, Y), or(Y, X))), true, or(Y, X), or(X, Y))
% 55.12/7.61 = { by lemma 16 }
% 55.12/7.61 fresh3(true, true, or(Y, X), or(X, Y))
% 55.12/7.61 = { by axiom 4 (rule_2) }
% 55.12/7.61 theorem(or(Y, X))
% 55.12/7.61
% 55.12/7.61 Lemma 18: axiom(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))) = true.
% 55.12/7.61 Proof:
% 55.12/7.61 axiom(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z))))
% 55.12/7.61 = { by axiom 3 (implies_definition) }
% 55.12/7.61 axiom(implies(implies(X, or(Y, Z)), or(Y, or(not(X), Z))))
% 55.12/7.61 = { by axiom 3 (implies_definition) }
% 55.12/7.61 axiom(implies(or(not(X), or(Y, Z)), or(Y, or(not(X), Z))))
% 55.12/7.61 = { by axiom 11 (axiom_1_5) }
% 55.12/7.61 true
% 55.12/7.61
% 55.12/7.61 Lemma 19: fresh(theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y))) = theorem(implies(or(Z, X), or(Z, Y))).
% 55.12/7.61 Proof:
% 55.12/7.61 fresh(theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y)))
% 55.12/7.61 = { by axiom 8 (rule_2) R->L }
% 55.12/7.61 fresh3(theorem(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh3(fresh2(axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 55.12/7.61 = { by axiom 10 (axiom_1_6) }
% 55.12/7.61 fresh3(fresh2(true, true, implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 fresh3(true, true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 55.12/7.61 = { by axiom 4 (rule_2) }
% 55.12/7.61 theorem(implies(or(Z, X), or(Z, Y)))
% 55.12/7.61
% 55.12/7.61 Lemma 20: fresh(theorem(or(X, or(Y, Z))), true, or(Y, or(X, Z))) = theorem(or(Y, or(X, Z))).
% 55.12/7.61 Proof:
% 55.12/7.61 fresh(theorem(or(X, or(Y, Z))), true, or(Y, or(X, Z)))
% 55.12/7.61 = { by axiom 8 (rule_2) R->L }
% 55.12/7.61 fresh3(theorem(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))), true, or(Y, or(X, Z)), or(X, or(Y, Z)))
% 55.12/7.61 = { by axiom 5 (rule_1) R->L }
% 55.12/7.61 fresh3(fresh2(axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))), true, implies(or(X, or(Y, Z)), or(Y, or(X, Z)))), true, or(Y, or(X, Z)), or(X, or(Y, Z)))
% 55.12/7.61 = { by axiom 11 (axiom_1_5) }
% 55.12/7.61 fresh3(fresh2(true, true, implies(or(X, or(Y, Z)), or(Y, or(X, Z)))), true, or(Y, or(X, Z)), or(X, or(Y, Z)))
% 55.12/7.61 = { by axiom 2 (rule_1) }
% 55.12/7.61 fresh3(true, true, or(Y, or(X, Z)), or(X, or(Y, Z)))
% 55.12/7.61 = { by axiom 4 (rule_2) }
% 55.12/7.61 theorem(or(Y, or(X, Z)))
% 55.12/7.61
% 55.12/7.61 Lemma 21: fresh(theorem(implies(X, or(Y, Z))), true, or(Y, implies(X, Z))) = theorem(or(Y, implies(X, Z))).
% 55.12/7.61 Proof:
% 55.12/7.61 fresh(theorem(implies(X, or(Y, Z))), true, or(Y, implies(X, Z)))
% 55.12/7.61 = { by axiom 8 (rule_2) R->L }
% 55.12/7.62 fresh3(theorem(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))), true, or(Y, implies(X, Z)), implies(X, or(Y, Z)))
% 55.12/7.62 = { by axiom 5 (rule_1) R->L }
% 55.12/7.62 fresh3(fresh2(axiom(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))), true, implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))), true, or(Y, implies(X, Z)), implies(X, or(Y, Z)))
% 55.12/7.62 = { by lemma 18 }
% 55.12/7.62 fresh3(fresh2(true, true, implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))), true, or(Y, implies(X, Z)), implies(X, or(Y, Z)))
% 55.12/7.62 = { by axiom 2 (rule_1) }
% 55.12/7.62 fresh3(true, true, or(Y, implies(X, Z)), implies(X, or(Y, Z)))
% 55.12/7.62 = { by axiom 4 (rule_2) }
% 55.12/7.62 theorem(or(Y, implies(X, Z)))
% 55.12/7.62
% 55.12/7.62 Goal 1 (prove_this): theorem(implies(implies(p, q), implies(or(p, q), q))) = true.
% 55.12/7.62 Proof:
% 55.12/7.62 theorem(implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.62 = { by axiom 4 (rule_2) R->L }
% 55.12/7.62 fresh3(true, true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 1 (rule_2) R->L }
% 55.12/7.62 fresh3(fresh(true, true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 1 (rule_2) R->L }
% 55.12/7.62 fresh3(fresh(fresh(true, true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 1 (rule_2) R->L }
% 55.12/7.62 fresh3(fresh(fresh(fresh(true, true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 1 (rule_2) R->L }
% 55.12/7.62 fresh3(fresh(fresh(fresh(fresh(true, true, implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by lemma 13 R->L }
% 55.12/7.62 fresh3(fresh(fresh(fresh(fresh(theorem(implies(q, implies(or(p, q), q))), true, implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 8 (rule_2) R->L }
% 55.12/7.62 fresh3(fresh(fresh(fresh(fresh3(theorem(implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 5 (rule_1) R->L }
% 55.12/7.62 fresh3(fresh(fresh(fresh(fresh3(fresh2(axiom(implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.62 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh(fresh(fresh(fresh3(fresh2(axiom(implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), or(not(p), implies(or(p, q), q))))), true, implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh(fresh(fresh(fresh3(fresh2(axiom(implies(implies(q, implies(or(p, q), q)), implies(or(not(p), q), or(not(p), implies(or(p, q), q))))), true, implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 10 (axiom_1_6) }
% 55.12/7.63 fresh3(fresh(fresh(fresh(fresh3(fresh2(true, true, implies(implies(q, implies(or(p, q), q)), implies(implies(p, q), implies(p, implies(or(p, q), q))))), true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 2 (rule_1) }
% 55.12/7.63 fresh3(fresh(fresh(fresh(fresh3(true, true, implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(q, implies(or(p, q), q))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 4 (rule_2) }
% 55.12/7.63 fresh3(fresh(fresh(fresh(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 8 (rule_2) R->L }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 5 (rule_1) R->L }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), or(not(p), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(implies(implies(p, q), or(not(p), implies(or(p, q), q))), or(not(p), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by lemma 18 }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(fresh2(true, true, implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 2 (rule_1) }
% 55.12/7.63 fresh3(fresh(fresh(fresh3(true, true, implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 4 (rule_2) }
% 55.12/7.63 fresh3(fresh(fresh(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by lemma 19 }
% 55.12/7.63 fresh3(fresh(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 8 (rule_2) R->L }
% 55.12/7.63 fresh3(fresh3(theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh3(theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 3 (implies_definition) }
% 55.12/7.63 fresh3(fresh3(theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by lemma 19 R->L }
% 55.12/7.63 fresh3(fresh3(fresh(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by lemma 14 }
% 55.12/7.63 fresh3(fresh3(fresh(true, true, implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.63 = { by axiom 1 (rule_2) }
% 55.12/7.63 fresh3(fresh3(true, true, implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.64 = { by axiom 4 (rule_2) }
% 55.12/7.64 fresh3(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, implies(implies(p, q), implies(or(p, q), q)), or(implies(implies(p, q), implies(or(p, q), q)), p))
% 55.12/7.64 = { by axiom 8 (rule_2) }
% 55.12/7.64 fresh(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 17 R->L }
% 55.12/7.64 fresh(fresh(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 21 R->L }
% 55.12/7.64 fresh(fresh(fresh(theorem(implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by axiom 4 (rule_2) R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh3(true, true, implies(implies(p, q), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 13 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh3(theorem(implies(or(p, implies(or(p, q), q)), implies(implies(p, q), or(p, implies(or(p, q), q))))), true, implies(implies(p, q), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by axiom 8 (rule_2) }
% 55.12/7.64 fresh(fresh(fresh(fresh(theorem(or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 21 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(theorem(implies(or(p, q), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by axiom 3 (implies_definition) }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(theorem(or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 17 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 15 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 20 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 17 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 15 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.64 = { by lemma 20 R->L }
% 55.12/7.64 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.65 = { by lemma 17 R->L }
% 55.12/7.65 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.65 = { by lemma 20 R->L }
% 55.12/7.65 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.65 = { by axiom 4 (rule_2) R->L }
% 55.12/7.65 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh3(true, true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.65 = { by lemma 12 R->L }
% 55.12/7.65 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh3(theorem(implies(or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))), or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.66 = { by axiom 8 (rule_2) }
% 55.12/7.66 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.66 = { by axiom 4 (rule_2) R->L }
% 55.12/7.66 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh3(true, true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))), implies(or(p, q), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.66 = { by lemma 16 R->L }
% 55.12/7.66 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh3(theorem(implies(or(not(or(p, q)), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))), implies(or(p, q), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.66 = { by axiom 3 (implies_definition) R->L }
% 55.12/7.66 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh3(theorem(implies(implies(or(p, q), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))), implies(or(p, q), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 8 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(theorem(implies(or(p, q), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by lemma 12 }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q)))), true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(p, q), not(or(p, q))), or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), not(or(p, q))))), true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(p, q)))), true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)), or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q)))), true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(or(p, q), not(or(p, q))), not(or(p, q))), or(p, q))), true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(p, q), or(or(or(p, q), not(or(p, q))), not(or(p, q))))), true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(or(p, q), not(or(p, q))), or(or(p, q), not(or(p, q))))), true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.67 fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(or(p, q), not(or(p, q)))), true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.67 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(not(or(p, q)), or(p, q))), true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(fresh(fresh(fresh(fresh(true, true, or(p, implies(or(p, q), q))), true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(fresh(fresh(fresh(true, true, implies(implies(p, q), or(p, implies(or(p, q), q)))), true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(fresh(fresh(true, true, or(p, implies(implies(p, q), implies(or(p, q), q)))), true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(fresh(true, true, or(implies(implies(p, q), implies(or(p, q), q)), p)), true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 fresh(true, true, implies(implies(p, q), implies(or(p, q), q)))
% 55.12/7.68 = { by axiom 1 (rule_2) }
% 55.12/7.68 true
% 55.12/7.68 % SZS output end Proof
% 55.12/7.68
% 55.12/7.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------