TSTP Solution File: LCL485+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL485+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n013.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 08:19:11 EDT 2023
% Result : Theorem 11.85s 1.90s
% Output : Proof 12.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL485+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 17:40:17 EDT 2023
% 0.16/0.34 % CPUTime :
% 11.85/1.90 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.85/1.90
% 11.85/1.90 % SZS status Theorem
% 11.85/1.90
% 11.85/1.94 % SZS output start Proof
% 11.85/1.94 Take the following subset of the input axioms:
% 11.85/1.94 fof(hilbert_implies_2, conjecture, implies_2).
% 11.85/1.94 fof(hilbert_op_implies_and, axiom, op_implies_and).
% 11.85/1.94 fof(hilbert_op_or, axiom, op_or).
% 11.85/1.94 fof(implies_2, axiom, implies_2 <=> ![X, Y]: is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))).
% 11.85/1.94 fof(modus_ponens, axiom, modus_ponens <=> ![X2, Y2]: ((is_a_theorem(X2) & is_a_theorem(implies(X2, Y2))) => is_a_theorem(Y2))).
% 11.85/1.94 fof(op_and, axiom, op_and => ![X2, Y2]: and(X2, Y2)=not(or(not(X2), not(Y2)))).
% 11.85/1.94 fof(op_implies_and, axiom, op_implies_and => ![X2, Y2]: implies(X2, Y2)=not(and(X2, not(Y2)))).
% 11.85/1.94 fof(op_implies_or, axiom, op_implies_or => ![X2, Y2]: implies(X2, Y2)=or(not(X2), Y2)).
% 11.85/1.94 fof(op_or, axiom, op_or => ![X2, Y2]: or(X2, Y2)=not(and(not(X2), not(Y2)))).
% 11.85/1.94 fof(principia_modus_ponens, axiom, modus_ponens).
% 11.85/1.94 fof(principia_op_and, axiom, op_and).
% 11.85/1.94 fof(principia_op_implies_or, axiom, op_implies_or).
% 11.85/1.94 fof(principia_r1, axiom, r1).
% 11.85/1.94 fof(principia_r2, axiom, r2).
% 11.85/1.94 fof(principia_r3, axiom, r3).
% 11.85/1.94 fof(principia_r4, axiom, r4).
% 11.85/1.94 fof(principia_r5, axiom, r5).
% 11.85/1.94 fof(r1, axiom, r1 <=> ![P]: is_a_theorem(implies(or(P, P), P))).
% 11.85/1.94 fof(r2, axiom, r2 <=> ![Q, P2]: is_a_theorem(implies(Q, or(P2, Q)))).
% 11.85/1.94 fof(r3, axiom, r3 <=> ![P2, Q2]: is_a_theorem(implies(or(P2, Q2), or(Q2, P2)))).
% 11.85/1.94 fof(r4, axiom, r4 <=> ![R, P2, Q2]: is_a_theorem(implies(or(P2, or(Q2, R)), or(Q2, or(P2, R))))).
% 11.85/1.94 fof(r5, axiom, r5 <=> ![P2, Q2, R2]: is_a_theorem(implies(implies(Q2, R2), implies(or(P2, Q2), or(P2, R2))))).
% 11.85/1.94
% 11.85/1.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.85/1.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.85/1.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.85/1.94 fresh(y, y, x1...xn) = u
% 11.85/1.94 C => fresh(s, t, x1...xn) = v
% 11.85/1.94 where fresh is a fresh function symbol and x1..xn are the free
% 11.85/1.94 variables of u and v.
% 11.85/1.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.85/1.94 input problem has no model of domain size 1).
% 11.85/1.94
% 11.85/1.94 The encoding turns the above axioms into the following unit equations and goals:
% 11.85/1.94
% 11.85/1.94 Axiom 1 (principia_modus_ponens): modus_ponens = true.
% 11.85/1.94 Axiom 2 (principia_r1): r1 = true.
% 11.85/1.94 Axiom 3 (principia_r2): r2 = true.
% 11.85/1.94 Axiom 4 (principia_r3): r3 = true.
% 11.85/1.94 Axiom 5 (principia_r4): r4 = true.
% 11.85/1.94 Axiom 6 (principia_r5): r5 = true.
% 11.85/1.94 Axiom 7 (hilbert_op_or): op_or = true.
% 11.85/1.94 Axiom 8 (principia_op_and): op_and = true.
% 11.85/1.94 Axiom 9 (hilbert_op_implies_and): op_implies_and = true.
% 11.85/1.94 Axiom 10 (principia_op_implies_or): op_implies_or = true.
% 11.85/1.94 Axiom 11 (implies_2): fresh38(X, X) = true.
% 11.85/1.94 Axiom 12 (modus_ponens_2): fresh60(X, X, Y) = true.
% 11.85/1.94 Axiom 13 (modus_ponens_2): fresh28(X, X, Y) = is_a_theorem(Y).
% 11.85/1.94 Axiom 14 (r1_1): fresh12(X, X, Y) = true.
% 11.85/1.94 Axiom 15 (modus_ponens_2): fresh59(X, X, Y, Z) = fresh60(modus_ponens, true, Z).
% 11.85/1.94 Axiom 16 (op_and): fresh24(X, X, Y, Z) = and(Y, Z).
% 11.85/1.94 Axiom 17 (op_implies_and): fresh22(X, X, Y, Z) = implies(Y, Z).
% 11.85/1.94 Axiom 18 (op_implies_and): fresh22(op_implies_and, true, X, Y) = not(and(X, not(Y))).
% 11.85/1.94 Axiom 19 (op_implies_or): fresh21(X, X, Y, Z) = implies(Y, Z).
% 11.85/1.94 Axiom 20 (op_implies_or): fresh21(op_implies_or, true, X, Y) = or(not(X), Y).
% 11.85/1.94 Axiom 21 (op_or): fresh20(X, X, Y, Z) = or(Y, Z).
% 11.85/1.94 Axiom 22 (r2_1): fresh10(X, X, Y, Z) = true.
% 11.85/1.94 Axiom 23 (r3_1): fresh8(X, X, Y, Z) = true.
% 11.85/1.94 Axiom 24 (r2_1): fresh10(r2, true, X, Y) = is_a_theorem(implies(Y, or(X, Y))).
% 11.85/1.94 Axiom 25 (r1_1): fresh12(r1, true, X) = is_a_theorem(implies(or(X, X), X)).
% 11.85/1.94 Axiom 26 (op_and): fresh24(op_and, true, X, Y) = not(or(not(X), not(Y))).
% 11.85/1.94 Axiom 27 (op_or): fresh20(op_or, true, X, Y) = not(and(not(X), not(Y))).
% 11.85/1.94 Axiom 28 (r4_1): fresh6(X, X, Y, Z, W) = true.
% 11.85/1.94 Axiom 29 (r5_1): fresh4(X, X, Y, Z, W) = true.
% 11.85/1.94 Axiom 30 (r3_1): fresh8(r3, true, X, Y) = is_a_theorem(implies(or(X, Y), or(Y, X))).
% 11.85/1.94 Axiom 31 (modus_ponens_2): fresh59(is_a_theorem(implies(X, Y)), true, X, Y) = fresh28(is_a_theorem(X), true, Y).
% 11.85/1.94 Axiom 32 (r5_1): fresh4(r5, true, X, Y, Z) = is_a_theorem(implies(implies(Y, Z), implies(or(X, Y), or(X, Z)))).
% 11.85/1.94 Axiom 33 (r4_1): fresh6(r4, true, X, Y, Z) = is_a_theorem(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))).
% 11.85/1.94 Axiom 34 (implies_2): fresh38(is_a_theorem(implies(implies(x11, implies(x11, y11)), implies(x11, y11))), true) = implies_2.
% 11.85/1.94
% 11.85/1.94 Lemma 35: not(and(X, not(Y))) = implies(X, Y).
% 11.85/1.94 Proof:
% 11.85/1.94 not(and(X, not(Y)))
% 11.85/1.94 = { by axiom 18 (op_implies_and) R->L }
% 11.85/1.94 fresh22(op_implies_and, true, X, Y)
% 11.85/1.94 = { by axiom 9 (hilbert_op_implies_and) }
% 11.85/1.94 fresh22(true, true, X, Y)
% 11.85/1.94 = { by axiom 17 (op_implies_and) }
% 11.85/1.94 implies(X, Y)
% 11.85/1.94
% 11.85/1.94 Lemma 36: implies(not(X), Y) = or(X, Y).
% 11.85/1.94 Proof:
% 11.85/1.94 implies(not(X), Y)
% 11.85/1.94 = { by lemma 35 R->L }
% 11.85/1.94 not(and(not(X), not(Y)))
% 11.85/1.94 = { by axiom 27 (op_or) R->L }
% 11.85/1.94 fresh20(op_or, true, X, Y)
% 11.85/1.94 = { by axiom 7 (hilbert_op_or) }
% 11.85/1.94 fresh20(true, true, X, Y)
% 11.85/1.94 = { by axiom 21 (op_or) }
% 11.85/1.95 or(X, Y)
% 11.85/1.95
% 11.85/1.95 Lemma 37: or(not(X), Y) = implies(X, Y).
% 11.85/1.95 Proof:
% 11.85/1.95 or(not(X), Y)
% 11.85/1.95 = { by axiom 20 (op_implies_or) R->L }
% 11.85/1.95 fresh21(op_implies_or, true, X, Y)
% 11.85/1.95 = { by axiom 10 (principia_op_implies_or) }
% 11.85/1.95 fresh21(true, true, X, Y)
% 11.85/1.95 = { by axiom 19 (op_implies_or) }
% 11.85/1.95 implies(X, Y)
% 11.85/1.95
% 11.85/1.95 Lemma 38: fresh59(X, X, Y, Z) = true.
% 11.85/1.95 Proof:
% 11.85/1.95 fresh59(X, X, Y, Z)
% 11.85/1.95 = { by axiom 15 (modus_ponens_2) }
% 11.85/1.95 fresh60(modus_ponens, true, Z)
% 11.85/1.95 = { by axiom 1 (principia_modus_ponens) }
% 11.85/1.95 fresh60(true, true, Z)
% 11.85/1.95 = { by axiom 12 (modus_ponens_2) }
% 11.85/1.95 true
% 11.85/1.95
% 11.85/1.95 Lemma 39: not(implies(X, not(Y))) = and(X, Y).
% 11.85/1.95 Proof:
% 11.85/1.95 not(implies(X, not(Y)))
% 11.85/1.95 = { by lemma 37 R->L }
% 11.85/1.95 not(or(not(X), not(Y)))
% 11.85/1.95 = { by axiom 26 (op_and) R->L }
% 11.85/1.95 fresh24(op_and, true, X, Y)
% 11.85/1.95 = { by axiom 8 (principia_op_and) }
% 11.85/1.95 fresh24(true, true, X, Y)
% 11.85/1.95 = { by axiom 16 (op_and) }
% 11.85/1.95 and(X, Y)
% 11.85/1.95
% 11.85/1.95 Lemma 40: implies(implies(X, not(Y)), Z) = or(and(X, Y), Z).
% 11.85/1.95 Proof:
% 11.85/1.95 implies(implies(X, not(Y)), Z)
% 11.85/1.95 = { by lemma 37 R->L }
% 11.85/1.95 or(not(implies(X, not(Y))), Z)
% 11.85/1.95 = { by lemma 39 }
% 11.85/1.95 or(and(X, Y), Z)
% 11.85/1.95
% 11.85/1.95 Lemma 41: or(implies(X, not(Y)), Z) = implies(and(X, Y), Z).
% 11.85/1.95 Proof:
% 11.85/1.95 or(implies(X, not(Y)), Z)
% 11.85/1.95 = { by lemma 36 R->L }
% 11.85/1.95 implies(not(implies(X, not(Y))), Z)
% 11.85/1.95 = { by lemma 39 }
% 11.85/1.95 implies(and(X, Y), Z)
% 11.85/1.95
% 11.85/1.95 Lemma 42: is_a_theorem(implies(or(X, Y), or(Y, X))) = true.
% 11.85/1.95 Proof:
% 11.85/1.95 is_a_theorem(implies(or(X, Y), or(Y, X)))
% 11.85/1.95 = { by axiom 30 (r3_1) R->L }
% 11.85/1.95 fresh8(r3, true, X, Y)
% 11.85/1.95 = { by axiom 4 (principia_r3) }
% 11.85/1.95 fresh8(true, true, X, Y)
% 11.85/1.95 = { by axiom 23 (r3_1) }
% 11.85/1.95 true
% 11.85/1.95
% 11.85/1.95 Lemma 43: is_a_theorem(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 11.85/1.95 Proof:
% 11.85/1.95 is_a_theorem(implies(implies(X, Y), implies(or(Z, X), or(Z, Y))))
% 11.85/1.95 = { by axiom 32 (r5_1) R->L }
% 11.85/1.95 fresh4(r5, true, Z, X, Y)
% 11.85/1.95 = { by axiom 6 (principia_r5) }
% 11.85/1.95 fresh4(true, true, Z, X, Y)
% 11.85/1.95 = { by axiom 29 (r5_1) }
% 11.85/1.95 true
% 11.85/1.95
% 11.85/1.95 Lemma 44: fresh28(is_a_theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y))) = true.
% 11.85/1.95 Proof:
% 11.85/1.95 fresh28(is_a_theorem(implies(X, Y)), true, implies(or(Z, X), or(Z, Y)))
% 11.85/1.95 = { by axiom 31 (modus_ponens_2) R->L }
% 11.85/1.95 fresh59(is_a_theorem(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))), true, implies(X, Y), implies(or(Z, X), or(Z, Y)))
% 11.85/1.95 = { by lemma 43 }
% 11.85/1.95 fresh59(true, true, implies(X, Y), implies(or(Z, X), or(Z, Y)))
% 11.85/1.95 = { by lemma 38 }
% 11.85/1.95 true
% 11.85/1.95
% 11.85/1.95 Goal 1 (hilbert_implies_2): implies_2 = true.
% 11.85/1.95 Proof:
% 11.85/1.95 implies_2
% 11.85/1.95 = { by axiom 34 (implies_2) R->L }
% 11.85/1.95 fresh38(is_a_theorem(implies(implies(x11, implies(x11, y11)), implies(x11, y11))), true)
% 11.85/1.95 = { by lemma 37 R->L }
% 11.85/1.95 fresh38(is_a_theorem(or(not(implies(x11, implies(x11, y11))), implies(x11, y11))), true)
% 11.85/1.95 = { by lemma 35 R->L }
% 11.85/1.95 fresh38(is_a_theorem(or(not(implies(x11, not(and(x11, not(y11))))), implies(x11, y11))), true)
% 11.85/1.95 = { by lemma 39 }
% 11.85/1.95 fresh38(is_a_theorem(or(and(x11, and(x11, not(y11))), implies(x11, y11))), true)
% 11.85/1.95 = { by lemma 35 R->L }
% 11.85/1.95 fresh38(is_a_theorem(or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by axiom 13 (modus_ponens_2) R->L }
% 11.85/1.95 fresh38(fresh28(true, true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 38 R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(true, true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 38 R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(true, true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by axiom 28 (r4_1) R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(fresh6(true, true, not(or(not(x11), not(and(x11, not(y11))))), and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11))))), true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by axiom 5 (principia_r4) R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(fresh6(r4, true, not(or(not(x11), not(and(x11, not(y11))))), and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11))))), true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by axiom 33 (r4_1) }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(is_a_theorem(implies(or(not(or(not(x11), not(and(x11, not(y11))))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), or(not(or(not(x11), not(and(x11, not(y11))))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))))), true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 37 }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), or(not(or(not(x11), not(and(x11, not(y11))))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))))), true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 37 }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))))), true, implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by axiom 31 (modus_ponens_2) }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh28(is_a_theorem(implies(or(not(x11), not(and(x11, not(y11)))), or(and(and(x11, not(y11)), not(x11)), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 40 R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh28(is_a_theorem(implies(or(not(x11), not(and(x11, not(y11)))), implies(implies(and(x11, not(y11)), not(not(x11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 36 R->L }
% 11.85/1.95 fresh38(fresh28(fresh59(fresh28(is_a_theorem(implies(implies(not(not(x11)), not(and(x11, not(y11)))), implies(implies(and(x11, not(y11)), not(not(x11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.95 = { by lemma 37 R->L }
% 11.85/1.96 fresh38(fresh28(fresh59(fresh28(is_a_theorem(implies(implies(not(not(x11)), not(and(x11, not(y11)))), implies(implies(and(x11, not(y11)), not(not(x11))), or(not(and(x11, not(y11))), not(and(x11, not(y11))))))), true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 37 R->L }
% 11.85/1.96 fresh38(fresh28(fresh59(fresh28(is_a_theorem(implies(implies(not(not(x11)), not(and(x11, not(y11)))), implies(or(not(and(x11, not(y11))), not(not(x11))), or(not(and(x11, not(y11))), not(and(x11, not(y11))))))), true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 43 }
% 11.85/1.96 fresh38(fresh28(fresh59(fresh28(true, true, or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by axiom 13 (modus_ponens_2) }
% 11.85/1.96 fresh38(fresh28(fresh59(is_a_theorem(or(and(and(x11, not(y11)), not(x11)), implies(or(not(x11), not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 37 }
% 11.85/1.96 fresh38(fresh28(fresh59(is_a_theorem(or(and(and(x11, not(y11)), not(x11)), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 36 R->L }
% 11.85/1.96 fresh38(fresh28(fresh59(is_a_theorem(implies(not(and(and(x11, not(y11)), not(x11))), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 35 }
% 11.85/1.96 fresh38(fresh28(fresh59(is_a_theorem(implies(implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11))))))), true, implies(and(x11, not(y11)), x11), implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by axiom 31 (modus_ponens_2) }
% 11.85/1.96 fresh38(fresh28(fresh28(is_a_theorem(implies(and(x11, not(y11)), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 41 R->L }
% 11.85/1.96 fresh38(fresh28(fresh28(is_a_theorem(or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by axiom 13 (modus_ponens_2) R->L }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(true, true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 38 R->L }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh59(true, true, implies(or(not(not(y11)), not(x11)), implies(x11, not(not(y11)))), or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 42 R->L }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(or(not(or(not(not(y11)), not(x11))), implies(x11, not(not(y11)))), or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11)))))), true, implies(or(not(not(y11)), not(x11)), implies(x11, not(not(y11)))), or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 37 }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(implies(or(not(not(y11)), not(x11)), implies(x11, not(not(y11)))), or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11)))))), true, implies(or(not(not(y11)), not(x11)), implies(x11, not(not(y11)))), or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by axiom 31 (modus_ponens_2) }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh28(is_a_theorem(implies(or(not(not(y11)), not(x11)), implies(x11, not(not(y11))))), true, or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 37 R->L }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh28(is_a_theorem(implies(or(not(not(y11)), not(x11)), or(not(x11), not(not(y11))))), true, or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 42 }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(fresh28(true, true, or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by axiom 13 (modus_ponens_2) }
% 11.85/1.96 fresh38(fresh28(fresh28(fresh28(is_a_theorem(or(implies(x11, not(not(y11))), not(or(not(not(y11)), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 11.85/1.96 = { by lemma 36 R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh28(is_a_theorem(or(implies(x11, not(not(y11))), not(implies(not(not(not(y11))), not(x11))))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by lemma 39 }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh28(is_a_theorem(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 31 (modus_ponens_2) R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(is_a_theorem(implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 13 (modus_ponens_2) R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(true, true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by lemma 38 R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh59(true, true, or(x11, implies(not(not(not(y11))), not(x11))), or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by lemma 42 R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh59(is_a_theorem(implies(or(x11, implies(not(not(not(y11))), not(x11))), or(implies(not(not(not(y11))), not(x11)), x11))), true, or(x11, implies(not(not(not(y11))), not(x11))), or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 31 (modus_ponens_2) }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(is_a_theorem(or(x11, implies(not(not(not(y11))), not(x11)))), true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by lemma 37 R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(is_a_theorem(or(x11, or(not(not(not(not(y11)))), not(x11)))), true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by lemma 36 R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(is_a_theorem(implies(not(x11), or(not(not(not(not(y11)))), not(x11)))), true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 24 (r2_1) R->L }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(fresh10(r2, true, not(not(not(not(y11)))), not(x11)), true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 3 (principia_r2) }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(fresh10(true, true, not(not(not(not(y11)))), not(x11)), true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.96 = { by axiom 22 (r2_1) }
% 12.53/1.96 fresh38(fresh28(fresh28(fresh59(fresh28(fresh28(true, true, or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 13 (modus_ponens_2) }
% 12.53/1.97 fresh38(fresh28(fresh28(fresh59(fresh28(is_a_theorem(or(implies(not(not(not(y11))), not(x11)), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 41 }
% 12.53/1.97 fresh38(fresh28(fresh28(fresh59(fresh28(is_a_theorem(implies(and(not(not(not(y11))), x11), x11)), true, implies(or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11))), true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 44 }
% 12.53/1.97 fresh38(fresh28(fresh28(fresh59(true, true, or(implies(x11, not(not(y11))), and(not(not(not(y11))), x11)), or(implies(x11, not(not(y11))), x11)), true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 38 }
% 12.53/1.97 fresh38(fresh28(fresh28(true, true, implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 13 (modus_ponens_2) }
% 12.53/1.97 fresh38(fresh28(is_a_theorem(implies(implies(x11, not(and(x11, not(y11)))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 40 }
% 12.53/1.97 fresh38(fresh28(is_a_theorem(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 31 (modus_ponens_2) R->L }
% 12.53/1.97 fresh38(fresh59(is_a_theorem(implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 13 (modus_ponens_2) R->L }
% 12.53/1.97 fresh38(fresh59(fresh28(true, true, implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 14 (r1_1) R->L }
% 12.53/1.97 fresh38(fresh59(fresh28(fresh12(true, true, not(and(x11, not(y11)))), true, implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 2 (principia_r1) R->L }
% 12.53/1.97 fresh38(fresh59(fresh28(fresh12(r1, true, not(and(x11, not(y11)))), true, implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by axiom 25 (r1_1) }
% 12.53/1.97 fresh38(fresh59(fresh28(is_a_theorem(implies(or(not(and(x11, not(y11))), not(and(x11, not(y11)))), not(and(x11, not(y11))))), true, implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 37 }
% 12.53/1.97 fresh38(fresh59(fresh28(is_a_theorem(implies(implies(and(x11, not(y11)), not(and(x11, not(y11)))), not(and(x11, not(y11))))), true, implies(or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11)))))), true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 44 }
% 12.53/1.97 fresh38(fresh59(true, true, or(and(x11, and(x11, not(y11))), implies(and(x11, not(y11)), not(and(x11, not(y11))))), or(and(x11, and(x11, not(y11))), not(and(x11, not(y11))))), true)
% 12.53/1.97 = { by lemma 38 }
% 12.53/1.97 fresh38(true, true)
% 12.53/1.97 = { by axiom 11 (implies_2) }
% 12.53/1.97 true
% 12.53/1.97 % SZS output end Proof
% 12.53/1.97
% 12.53/1.97 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------