TSTP Solution File: LCL497+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL497+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 08:19:13 EDT 2023
% Result : Theorem 9.92s 1.71s
% Output : Proof 10.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL497+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 18:16:17 EDT 2023
% 0.11/0.33 % CPUTime :
% 9.92/1.71 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 9.92/1.71
% 9.92/1.71 % SZS status Theorem
% 9.92/1.71
% 10.69/1.72 % SZS output start Proof
% 10.69/1.72 Take the following subset of the input axioms:
% 10.69/1.72 fof(cn2, axiom, cn2 <=> ![P, Q]: is_a_theorem(implies(P, implies(not(P), Q)))).
% 10.69/1.72 fof(luka_cn2, conjecture, cn2).
% 10.69/1.72 fof(modus_ponens, axiom, modus_ponens <=> ![X, Y]: ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))).
% 10.69/1.72 fof(op_implies_or, axiom, op_implies_or => ![X2, Y2]: implies(X2, Y2)=or(not(X2), Y2)).
% 10.69/1.72 fof(principia_modus_ponens, axiom, modus_ponens).
% 10.69/1.72 fof(principia_op_implies_or, axiom, op_implies_or).
% 10.69/1.72 fof(principia_r2, axiom, r2).
% 10.69/1.72 fof(principia_r3, axiom, r3).
% 10.69/1.72 fof(principia_r4, axiom, r4).
% 10.69/1.72 fof(principia_r5, axiom, r5).
% 10.69/1.72 fof(r2, axiom, r2 <=> ![P2, Q2]: is_a_theorem(implies(Q2, or(P2, Q2)))).
% 10.69/1.72 fof(r3, axiom, r3 <=> ![P2, Q2]: is_a_theorem(implies(or(P2, Q2), or(Q2, P2)))).
% 10.69/1.72 fof(r4, axiom, r4 <=> ![R, P2, Q2]: is_a_theorem(implies(or(P2, or(Q2, R)), or(Q2, or(P2, R))))).
% 10.69/1.72 fof(r5, axiom, r5 <=> ![P2, Q2, R2]: is_a_theorem(implies(implies(Q2, R2), implies(or(P2, Q2), or(P2, R2))))).
% 10.69/1.72
% 10.69/1.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.69/1.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.69/1.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.69/1.72 fresh(y, y, x1...xn) = u
% 10.69/1.72 C => fresh(s, t, x1...xn) = v
% 10.69/1.72 where fresh is a fresh function symbol and x1..xn are the free
% 10.69/1.72 variables of u and v.
% 10.69/1.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.69/1.72 input problem has no model of domain size 1).
% 10.69/1.72
% 10.69/1.72 The encoding turns the above axioms into the following unit equations and goals:
% 10.69/1.72
% 10.69/1.72 Axiom 1 (principia_modus_ponens): modus_ponens = true.
% 10.69/1.72 Axiom 2 (principia_r2): r2 = true.
% 10.69/1.72 Axiom 3 (principia_r3): r3 = true.
% 10.69/1.72 Axiom 4 (principia_r4): r4 = true.
% 10.69/1.72 Axiom 5 (principia_r5): r5 = true.
% 10.69/1.72 Axiom 6 (principia_op_implies_or): op_implies_or = true.
% 10.69/1.72 Axiom 7 (cn2): fresh50(X, X) = true.
% 10.69/1.72 Axiom 8 (modus_ponens_2): fresh60(X, X, Y) = true.
% 10.69/1.72 Axiom 9 (modus_ponens_2): fresh28(X, X, Y) = is_a_theorem(Y).
% 10.69/1.72 Axiom 10 (modus_ponens_2): fresh59(X, X, Y, Z) = fresh60(modus_ponens, true, Z).
% 10.69/1.72 Axiom 11 (op_implies_or): fresh21(X, X, Y, Z) = implies(Y, Z).
% 10.69/1.72 Axiom 12 (op_implies_or): fresh21(op_implies_or, true, X, Y) = or(not(X), Y).
% 10.69/1.72 Axiom 13 (r2_1): fresh10(X, X, Y, Z) = true.
% 10.69/1.72 Axiom 14 (r3_1): fresh8(X, X, Y, Z) = true.
% 10.69/1.72 Axiom 15 (r2_1): fresh10(r2, true, X, Y) = is_a_theorem(implies(Y, or(X, Y))).
% 10.69/1.72 Axiom 16 (r4_1): fresh6(X, X, Y, Z, W) = true.
% 10.69/1.72 Axiom 17 (r5_1): fresh4(X, X, Y, Z, W) = true.
% 10.69/1.72 Axiom 18 (r3_1): fresh8(r3, true, X, Y) = is_a_theorem(implies(or(X, Y), or(Y, X))).
% 10.69/1.72 Axiom 19 (modus_ponens_2): fresh59(is_a_theorem(implies(X, Y)), true, X, Y) = fresh28(is_a_theorem(X), true, Y).
% 10.69/1.72 Axiom 20 (cn2): fresh50(is_a_theorem(implies(p7, implies(not(p7), q5))), true) = cn2.
% 10.69/1.72 Axiom 21 (r5_1): fresh4(r5, true, X, Y, Z) = is_a_theorem(implies(implies(Y, Z), implies(or(X, Y), or(X, Z)))).
% 10.69/1.72 Axiom 22 (r4_1): fresh6(r4, true, X, Y, Z) = is_a_theorem(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))).
% 10.69/1.72
% 10.69/1.72 Lemma 23: or(not(X), Y) = implies(X, Y).
% 10.69/1.72 Proof:
% 10.69/1.72 or(not(X), Y)
% 10.69/1.72 = { by axiom 12 (op_implies_or) R->L }
% 10.69/1.72 fresh21(op_implies_or, true, X, Y)
% 10.69/1.72 = { by axiom 6 (principia_op_implies_or) }
% 10.69/1.72 fresh21(true, true, X, Y)
% 10.69/1.72 = { by axiom 11 (op_implies_or) }
% 10.69/1.72 implies(X, Y)
% 10.69/1.72
% 10.69/1.72 Lemma 24: fresh59(X, X, Y, Z) = true.
% 10.69/1.72 Proof:
% 10.69/1.72 fresh59(X, X, Y, Z)
% 10.69/1.72 = { by axiom 10 (modus_ponens_2) }
% 10.69/1.72 fresh60(modus_ponens, true, Z)
% 10.69/1.72 = { by axiom 1 (principia_modus_ponens) }
% 10.69/1.72 fresh60(true, true, Z)
% 10.69/1.72 = { by axiom 8 (modus_ponens_2) }
% 10.69/1.72 true
% 10.69/1.72
% 10.69/1.72 Lemma 25: is_a_theorem(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z)))) = true.
% 10.69/1.72 Proof:
% 10.69/1.72 is_a_theorem(implies(implies(X, or(Y, Z)), or(Y, implies(X, Z))))
% 10.69/1.72 = { by lemma 23 R->L }
% 10.69/1.72 is_a_theorem(implies(implies(X, or(Y, Z)), or(Y, or(not(X), Z))))
% 10.69/1.72 = { by lemma 23 R->L }
% 10.69/1.72 is_a_theorem(implies(or(not(X), or(Y, Z)), or(Y, or(not(X), Z))))
% 10.69/1.72 = { by axiom 22 (r4_1) R->L }
% 10.69/1.72 fresh6(r4, true, not(X), Y, Z)
% 10.69/1.72 = { by axiom 4 (principia_r4) }
% 10.69/1.72 fresh6(true, true, not(X), Y, Z)
% 10.69/1.72 = { by axiom 16 (r4_1) }
% 10.69/1.72 true
% 10.69/1.72
% 10.69/1.72 Goal 1 (luka_cn2): cn2 = true.
% 10.69/1.72 Proof:
% 10.69/1.72 cn2
% 10.69/1.72 = { by axiom 20 (cn2) R->L }
% 10.69/1.72 fresh50(is_a_theorem(implies(p7, implies(not(p7), q5))), true)
% 10.69/1.72 = { by lemma 23 R->L }
% 10.69/1.72 fresh50(is_a_theorem(or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.72 = { by axiom 9 (modus_ponens_2) R->L }
% 10.69/1.72 fresh50(fresh28(true, true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.72 = { by lemma 24 R->L }
% 10.69/1.72 fresh50(fresh28(fresh59(true, true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 24 R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(true, true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 24 R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh59(true, true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 25 R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh59(is_a_theorem(implies(implies(implies(or(q5, not(p7)), or(not(p7), q5)), or(not(implies(not(p7), or(q5, not(p7)))), implies(not(p7), or(not(p7), q5)))), or(not(implies(not(p7), or(q5, not(p7)))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))))), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 23 }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh59(is_a_theorem(implies(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), or(not(implies(not(p7), or(q5, not(p7)))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))))), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 23 }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh59(is_a_theorem(implies(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))))), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5)))), implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 19 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(is_a_theorem(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), implies(not(p7), or(not(p7), q5))))), true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 23 R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(is_a_theorem(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(implies(not(p7), or(q5, not(p7))), or(not(not(p7)), or(not(p7), q5))))), true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 23 R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(is_a_theorem(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(or(not(not(p7)), or(q5, not(p7))), or(not(not(p7)), or(not(p7), q5))))), true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 21 (r5_1) R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(fresh4(r5, true, not(not(p7)), or(q5, not(p7)), or(not(p7), q5)), true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 5 (principia_r5) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(fresh4(true, true, not(not(p7)), or(q5, not(p7)), or(not(p7), q5)), true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 17 (r5_1) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(fresh28(true, true, implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 9 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))))), true, implies(not(p7), or(q5, not(p7))), implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 19 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh28(is_a_theorem(implies(not(p7), or(q5, not(p7)))), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 15 (r2_1) R->L }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh28(fresh10(r2, true, q5, not(p7)), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 2 (principia_r2) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh28(fresh10(true, true, q5, not(p7)), true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 13 (r2_1) }
% 10.69/1.73 fresh50(fresh28(fresh59(fresh28(true, true, implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 9 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(fresh59(is_a_theorem(implies(implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5)))), true, implies(or(q5, not(p7)), or(not(p7), q5)), implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 19 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(fresh28(is_a_theorem(implies(or(q5, not(p7)), or(not(p7), q5))), true, implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 18 (r3_1) R->L }
% 10.69/1.73 fresh50(fresh28(fresh28(fresh8(r3, true, q5, not(p7)), true, implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 3 (principia_r3) }
% 10.69/1.73 fresh50(fresh28(fresh28(fresh8(true, true, q5, not(p7)), true, implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 14 (r3_1) }
% 10.69/1.73 fresh50(fresh28(fresh28(true, true, implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 9 (modus_ponens_2) }
% 10.69/1.73 fresh50(fresh28(is_a_theorem(implies(not(p7), or(not(p7), q5))), true, or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by axiom 19 (modus_ponens_2) R->L }
% 10.69/1.73 fresh50(fresh59(is_a_theorem(implies(implies(not(p7), or(not(p7), q5)), or(not(p7), implies(not(p7), q5)))), true, implies(not(p7), or(not(p7), q5)), or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 25 }
% 10.69/1.73 fresh50(fresh59(true, true, implies(not(p7), or(not(p7), q5)), or(not(p7), implies(not(p7), q5))), true)
% 10.69/1.73 = { by lemma 24 }
% 10.69/1.73 fresh50(true, true)
% 10.69/1.73 = { by axiom 7 (cn2) }
% 10.69/1.73 true
% 10.69/1.73 % SZS output end Proof
% 10.69/1.73
% 10.69/1.73 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------