TSTP Solution File: LCL199-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL199-3 : 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 : n031.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 08:17:57 EDT 2023
% Result : Unsatisfiable 183.77s 23.86s
% Output : Proof 184.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL199-3 : TPTP v8.1.2. Released v2.3.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 18:04:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 183.77/23.86 Command-line arguments: --flatten
% 183.77/23.86
% 183.77/23.86 % SZS status Unsatisfiable
% 183.77/23.86
% 183.77/23.90 % SZS output start Proof
% 183.77/23.90 Take the following subset of the input axioms:
% 183.77/23.90 fof(axiom_1_2, axiom, ![A]: axiom(implies(or(A, A), A))).
% 183.77/23.90 fof(axiom_1_3, axiom, ![B, A2]: axiom(implies(A2, or(B, A2)))).
% 183.77/23.90 fof(axiom_1_4, axiom, ![A2, B2]: axiom(implies(or(A2, B2), or(B2, A2)))).
% 183.77/23.90 fof(axiom_1_5, axiom, ![C, A2, B2]: axiom(implies(or(A2, or(B2, C)), or(B2, or(A2, C))))).
% 183.77/23.90 fof(axiom_1_6, axiom, ![A2, B2, C2]: axiom(implies(implies(A2, B2), implies(or(C2, A2), or(C2, B2))))).
% 183.77/23.90 fof(implies_definition, axiom, ![X, Y]: implies(X, Y)=or(not(X), Y)).
% 183.77/23.90 fof(prove_this, negated_conjecture, ~theorem(implies(not(or(p, q)), not(p)))).
% 183.77/23.90 fof(rule_1, axiom, ![X2]: (theorem(X2) | ~axiom(X2))).
% 183.77/23.90 fof(rule_2, axiom, ![X2, Y2]: (theorem(X2) | (~theorem(implies(Y2, X2)) | ~theorem(Y2)))).
% 183.77/23.90
% 183.77/23.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 183.77/23.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 183.77/23.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 183.77/23.90 fresh(y, y, x1...xn) = u
% 183.77/23.90 C => fresh(s, t, x1...xn) = v
% 183.77/23.90 where fresh is a fresh function symbol and x1..xn are the free
% 183.77/23.90 variables of u and v.
% 183.77/23.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 183.77/23.90 input problem has no model of domain size 1).
% 183.77/23.90
% 183.77/23.90 The encoding turns the above axioms into the following unit equations and goals:
% 183.77/23.90
% 183.77/23.90 Axiom 1 (rule_2): fresh(X, X, Y) = true.
% 183.77/23.90 Axiom 2 (rule_1): fresh2(X, X, Y) = true.
% 183.77/23.90 Axiom 3 (implies_definition): implies(X, Y) = or(not(X), Y).
% 183.77/23.90 Axiom 4 (rule_2): fresh3(X, X, Y, Z) = theorem(Y).
% 183.77/23.90 Axiom 5 (rule_1): fresh2(axiom(X), true, X) = theorem(X).
% 183.77/23.90 Axiom 6 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 183.77/23.90 Axiom 7 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 183.77/23.90 Axiom 8 (rule_2): fresh3(theorem(implies(X, Y)), true, Y, X) = fresh(theorem(X), true, Y).
% 183.77/23.90 Axiom 9 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 183.77/23.90 Axiom 10 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 183.77/23.90 Axiom 11 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 183.77/23.90
% 183.77/23.90 Lemma 12: theorem(implies(X, implies(Y, X))) = true.
% 183.77/23.90 Proof:
% 183.77/23.90 theorem(implies(X, implies(Y, X)))
% 183.77/23.90 = { by axiom 5 (rule_1) R->L }
% 183.77/23.90 fresh2(axiom(implies(X, implies(Y, X))), true, implies(X, implies(Y, X)))
% 183.77/23.90 = { by axiom 3 (implies_definition) }
% 183.77/23.90 fresh2(axiom(implies(X, or(not(Y), X))), true, implies(X, implies(Y, X)))
% 183.77/23.90 = { by axiom 6 (axiom_1_3) }
% 183.77/23.90 fresh2(true, true, implies(X, implies(Y, X)))
% 183.77/23.90 = { by axiom 2 (rule_1) }
% 183.77/23.90 true
% 183.77/23.90
% 183.77/23.90 Lemma 13: theorem(implies(or(X, Y), or(Y, X))) = true.
% 183.77/23.90 Proof:
% 183.77/23.90 theorem(implies(or(X, Y), or(Y, X)))
% 183.77/23.90 = { by axiom 5 (rule_1) R->L }
% 183.77/23.90 fresh2(axiom(implies(or(X, Y), or(Y, X))), true, implies(or(X, Y), or(Y, X)))
% 183.77/23.90 = { by axiom 9 (axiom_1_4) }
% 183.77/23.90 fresh2(true, true, implies(or(X, Y), or(Y, X)))
% 183.77/23.90 = { by axiom 2 (rule_1) }
% 183.77/23.90 true
% 183.77/23.90
% 183.77/23.90 Lemma 14: fresh(theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y))) = theorem(implies(or(Z, X), or(Z, Y))).
% 183.77/23.90 Proof:
% 183.77/23.90 fresh(theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y)))
% 183.77/23.90 = { by axiom 8 (rule_2) R->L }
% 183.77/23.90 fresh3(theorem(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 183.77/23.90 = { by axiom 5 (rule_1) R->L }
% 183.77/23.90 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))
% 183.77/23.90 = { by axiom 10 (axiom_1_6) }
% 183.77/23.90 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))
% 183.77/23.90 = { by axiom 2 (rule_1) }
% 183.77/23.90 fresh3(true, true, implies(or(Z, X), or(Z, Y)), implies(X, Y))
% 183.77/23.90 = { by axiom 4 (rule_2) }
% 183.77/23.90 theorem(implies(or(Z, X), or(Z, Y)))
% 183.77/23.90
% 183.77/23.90 Goal 1 (prove_this): theorem(implies(not(or(p, q)), not(p))) = true.
% 183.77/23.90 Proof:
% 183.77/23.90 theorem(implies(not(or(p, q)), not(p)))
% 183.77/23.90 = { by axiom 4 (rule_2) R->L }
% 183.77/23.90 fresh3(true, true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.90 = { by axiom 1 (rule_2) R->L }
% 183.77/23.90 fresh3(fresh(true, true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.90 = { by axiom 1 (rule_2) R->L }
% 183.77/23.90 fresh3(fresh(fresh(true, true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.90 = { by axiom 1 (rule_2) R->L }
% 183.77/23.90 fresh3(fresh(fresh(fresh(true, true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.90 = { by axiom 1 (rule_2) R->L }
% 183.77/23.90 fresh3(fresh(fresh(fresh(fresh(true, true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.90 = { by axiom 1 (rule_2) R->L }
% 183.77/23.90 fresh3(fresh(fresh(fresh(fresh(fresh(true, true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 1 (rule_2) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh(true, true, or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 2 (rule_1) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh(fresh2(true, true, implies(p, or(q, p))), true, or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 6 (axiom_1_3) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh(fresh2(axiom(implies(p, or(q, p))), true, implies(p, or(q, p))), true, or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 5 (rule_1) }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh(theorem(implies(p, or(q, p))), true, or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 3 (implies_definition) }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh(theorem(or(not(p), or(q, p))), true, or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 8 (rule_2) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh3(theorem(implies(or(not(p), or(q, p)), or(not(p), or(p, q)))), true, or(not(p), or(p, q)), or(not(p), or(q, p))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by lemma 14 R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh3(fresh(theorem(implies(or(q, p), or(p, q))), true, implies(or(not(p), or(q, p)), or(not(p), or(p, q)))), true, or(not(p), or(p, q)), or(not(p), or(q, p))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by lemma 13 }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh3(fresh(true, true, implies(or(not(p), or(q, p)), or(not(p), or(p, q)))), true, or(not(p), or(p, q)), or(not(p), or(q, p))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 1 (rule_2) }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(fresh3(true, true, or(not(p), or(p, q)), or(not(p), or(q, p))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 4 (rule_2) }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(theorem(or(not(p), or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 3 (implies_definition) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh(theorem(implies(p, or(p, q))), true, or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 8 (rule_2) R->L }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh3(theorem(implies(implies(p, or(p, q)), or(or(p, q), not(p)))), true, or(or(p, q), not(p)), implies(p, or(p, q))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 183.77/23.91 = { by axiom 3 (implies_definition) }
% 183.77/23.91 fresh3(fresh(fresh(fresh(fresh(fresh3(theorem(implies(or(not(p), or(p, q)), or(or(p, q), not(p)))), true, or(or(p, q), not(p)), implies(p, or(p, q))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.91 = { by lemma 13 }
% 184.28/23.91 fresh3(fresh(fresh(fresh(fresh(fresh3(true, true, or(or(p, q), not(p)), implies(p, or(p, q))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 4 (rule_2) }
% 184.28/23.92 fresh3(fresh(fresh(fresh(fresh(theorem(or(or(p, q), not(p))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 8 (rule_2) R->L }
% 184.28/23.92 fresh3(fresh(fresh(fresh(fresh3(theorem(implies(or(or(p, q), not(p)), or(or(p, q), implies(implies(p, not(or(p, q))), not(p))))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p))), or(or(p, q), not(p))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by lemma 14 R->L }
% 184.28/23.92 fresh3(fresh(fresh(fresh(fresh3(fresh(theorem(implies(not(p), implies(implies(p, not(or(p, q))), not(p)))), true, implies(or(or(p, q), not(p)), or(or(p, q), implies(implies(p, not(or(p, q))), not(p))))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p))), or(or(p, q), not(p))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by lemma 12 }
% 184.28/23.92 fresh3(fresh(fresh(fresh(fresh3(fresh(true, true, implies(or(or(p, q), not(p)), or(or(p, q), implies(implies(p, not(or(p, q))), not(p))))), true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p))), or(or(p, q), not(p))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 1 (rule_2) }
% 184.28/23.92 fresh3(fresh(fresh(fresh(fresh3(true, true, or(or(p, q), implies(implies(p, not(or(p, q))), not(p))), or(or(p, q), not(p))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 4 (rule_2) }
% 184.28/23.92 fresh3(fresh(fresh(fresh(theorem(or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 8 (rule_2) R->L }
% 184.28/23.92 fresh3(fresh(fresh(fresh3(theorem(implies(or(or(p, q), implies(implies(p, not(or(p, q))), not(p))), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q)))), true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q)), or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by lemma 13 }
% 184.28/23.92 fresh3(fresh(fresh(fresh3(true, true, or(implies(implies(p, not(or(p, q))), not(p)), or(p, q)), or(or(p, q), implies(implies(p, not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 4 (rule_2) }
% 184.28/23.92 fresh3(fresh(fresh(theorem(or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 8 (rule_2) R->L }
% 184.28/23.92 fresh3(fresh(fresh3(theorem(implies(or(implies(implies(p, not(or(p, q))), not(p)), or(p, q)), implies(implies(p, not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.92 = { by axiom 3 (implies_definition) }
% 184.28/23.92 fresh3(fresh(fresh3(theorem(implies(or(implies(implies(p, not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.93 = { by axiom 3 (implies_definition) }
% 184.28/23.93 fresh3(fresh(fresh3(theorem(implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.93 = { by axiom 4 (rule_2) R->L }
% 184.28/23.93 fresh3(fresh(fresh3(fresh3(true, true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.93 = { by axiom 1 (rule_2) R->L }
% 184.28/23.93 fresh3(fresh(fresh3(fresh3(fresh(true, true, implies(or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.93 = { by axiom 2 (rule_1) R->L }
% 184.28/23.93 fresh3(fresh(fresh3(fresh3(fresh(fresh2(true, true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.93 = { by axiom 7 (axiom_1_2) R->L }
% 184.28/23.94 fresh3(fresh(fresh3(fresh3(fresh(fresh2(axiom(implies(or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 5 (rule_1) }
% 184.28/23.94 fresh3(fresh(fresh3(fresh3(fresh(theorem(implies(or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by lemma 14 }
% 184.28/23.94 fresh3(fresh(fresh3(fresh3(theorem(implies(or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 3 (implies_definition) R->L }
% 184.28/23.94 fresh3(fresh(fresh3(fresh3(theorem(implies(implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), or(not(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q))), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 3 (implies_definition) R->L }
% 184.28/23.94 fresh3(fresh(fresh3(fresh3(theorem(implies(implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p)))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 8 (rule_2) }
% 184.28/23.94 fresh3(fresh(fresh3(fresh(theorem(implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by lemma 14 R->L }
% 184.28/23.94 fresh3(fresh(fresh3(fresh(fresh(theorem(implies(or(p, q), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 3 (implies_definition) }
% 184.28/23.94 fresh3(fresh(fresh3(fresh(fresh(theorem(or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.94 = { by axiom 4 (rule_2) R->L }
% 184.28/23.94 fresh3(fresh(fresh3(fresh(fresh(fresh3(true, true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 2 (rule_1) R->L }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh3(fresh2(true, true, implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 11 (axiom_1_5) R->L }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(or(not(or(not(p), not(or(p, q)))), or(not(or(p, q)), not(p))), or(not(or(p, q)), or(not(or(not(p), not(or(p, q)))), not(p))))), true, implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 3 (implies_definition) R->L }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), or(not(or(not(p), not(or(p, q)))), not(p))))), true, implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 3 (implies_definition) R->L }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh3(fresh2(axiom(implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 5 (rule_1) }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh3(theorem(implies(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p))), or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p))), implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 8 (rule_2) }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh(theorem(implies(or(not(p), not(or(p, q))), or(not(or(p, q)), not(p)))), true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by lemma 13 }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(fresh(true, true, or(not(or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 1 (rule_2) }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(fresh(true, true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), or(implies(or(not(p), not(or(p, q))), not(p)), implies(or(not(p), not(or(p, q))), not(p))))), true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 1 (rule_2) }
% 184.28/23.95 fresh3(fresh(fresh3(fresh(true, true, implies(or(implies(or(not(p), not(or(p, q))), not(p)), or(p, q)), implies(or(not(p), not(or(p, q))), not(p)))), true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 1 (rule_2) }
% 184.28/23.95 fresh3(fresh(fresh3(true, true, implies(implies(p, not(or(p, q))), not(p)), or(implies(implies(p, not(or(p, q))), not(p)), or(p, q))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 4 (rule_2) }
% 184.28/23.95 fresh3(fresh(theorem(implies(implies(p, not(or(p, q))), not(p))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 8 (rule_2) R->L }
% 184.28/23.95 fresh3(fresh3(theorem(implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 5 (rule_1) R->L }
% 184.28/23.95 fresh3(fresh3(fresh2(axiom(implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.95 = { by axiom 3 (implies_definition) }
% 184.28/23.96 fresh3(fresh3(fresh2(axiom(implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), or(not(not(or(p, q))), not(p))))), true, implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.96 = { by axiom 3 (implies_definition) }
% 184.28/23.96 fresh3(fresh3(fresh2(axiom(implies(implies(implies(p, not(or(p, q))), not(p)), implies(or(not(not(or(p, q))), implies(p, not(or(p, q)))), or(not(not(or(p, q))), not(p))))), true, implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.96 = { by axiom 10 (axiom_1_6) }
% 184.28/23.96 fresh3(fresh3(fresh2(true, true, implies(implies(implies(p, not(or(p, q))), not(p)), implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))))), true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.96 = { by axiom 2 (rule_1) }
% 184.28/23.96 fresh3(fresh3(true, true, implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p))), implies(implies(p, not(or(p, q))), not(p))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.96 = { by axiom 4 (rule_2) }
% 184.28/23.96 fresh3(theorem(implies(implies(not(or(p, q)), implies(p, not(or(p, q)))), implies(not(or(p, q)), not(p)))), true, implies(not(or(p, q)), not(p)), implies(not(or(p, q)), implies(p, not(or(p, q)))))
% 184.28/23.96 = { by axiom 8 (rule_2) }
% 184.28/23.96 fresh(theorem(implies(not(or(p, q)), implies(p, not(or(p, q))))), true, implies(not(or(p, q)), not(p)))
% 184.28/23.96 = { by lemma 12 }
% 184.28/23.96 fresh(true, true, implies(not(or(p, q)), not(p)))
% 184.28/23.96 = { by axiom 1 (rule_2) }
% 184.28/23.96 true
% 184.28/23.96 % SZS output end Proof
% 184.28/23.96
% 184.28/23.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------