TSTP Solution File: LCL927-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL927-1 : TPTP v8.1.2. Released v6.4.0.
% 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 : n007.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 08:21:12 EDT 2023
% Result : Unsatisfiable 188.57s 24.46s
% Output : Proof 191.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL927-1 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 06:16:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 188.57/24.46 Command-line arguments: --no-flatten-goal
% 188.57/24.46
% 188.57/24.46 % SZS status Unsatisfiable
% 188.57/24.46
% 189.74/24.56 % SZS output start Proof
% 189.74/24.56 Take the following subset of the input axioms:
% 189.74/24.56 fof(axBp, axiom, ![A, B, C]: p(i(i(A, B), i(i(B, C), i(A, C))))).
% 189.74/24.56 fof(axK_axC, negated_conjecture, ![B2, C2, A3]: (~p(i(c1, i(c2, c1))) | ~p(i(i(A3, i(B2, C2)), i(B2, i(A3, C2)))))).
% 189.74/24.56 fof(axL, axiom, ![X, Y]: p(i(i(i(X, Y), Y), i(i(Y, X), X)))).
% 189.74/24.56 fof(axTO, axiom, ![X2, Y2]: p(i(i(i(X2, Y2), i(Y2, X2)), i(Y2, X2)))).
% 189.74/24.56 fof(modus_ponens, axiom, ![A2, B2]: (~p(i(A2, B2)) | (~p(A2) | p(B2)))).
% 189.74/24.56 fof(resid1, axiom, ![B2, C2, A2_2]: (~p(i(f(A2_2, B2), C2)) | p(i(A2_2, i(B2, C2))))).
% 189.74/24.56 fof(resid2, axiom, ![B2, C2, A2_2]: (p(i(f(A2_2, B2), C2)) | ~p(i(A2_2, i(B2, C2))))).
% 189.74/24.56
% 189.74/24.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 189.74/24.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 189.74/24.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 189.74/24.56 fresh(y, y, x1...xn) = u
% 189.74/24.56 C => fresh(s, t, x1...xn) = v
% 189.74/24.56 where fresh is a fresh function symbol and x1..xn are the free
% 189.74/24.56 variables of u and v.
% 189.74/24.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 189.74/24.56 input problem has no model of domain size 1).
% 189.74/24.56
% 189.74/24.56 The encoding turns the above axioms into the following unit equations and goals:
% 189.74/24.56
% 189.74/24.56 Axiom 1 (modus_ponens): fresh4(X, X, Y) = true2.
% 189.74/24.56 Axiom 2 (modus_ponens): fresh3(X, X, Y, Z) = p(Z).
% 189.74/24.56 Axiom 3 (resid2): fresh(X, X, Y, Z, W) = true2.
% 189.74/24.56 Axiom 4 (resid1): fresh2(X, X, Y, Z, W) = true2.
% 189.74/24.56 Axiom 5 (modus_ponens): fresh3(p(i(X, Y)), true2, X, Y) = fresh4(p(X), true2, Y).
% 189.74/24.56 Axiom 6 (resid2): fresh(p(i(X, i(Y, Z))), true2, X, Y, Z) = p(i(f(X, Y), Z)).
% 189.74/24.56 Axiom 7 (resid1): fresh2(p(i(f(X, Y), Z)), true2, X, Y, Z) = p(i(X, i(Y, Z))).
% 189.74/24.56 Axiom 8 (axBp): p(i(i(X, Y), i(i(Y, Z), i(X, Z)))) = true2.
% 189.74/24.56 Axiom 9 (axL): p(i(i(i(X, Y), Y), i(i(Y, X), X))) = true2.
% 189.74/24.56 Axiom 10 (axTO): p(i(i(i(X, Y), i(Y, X)), i(Y, X))) = true2.
% 189.74/24.56
% 189.74/24.56 Lemma 11: fresh4(p(i(i(X, Y), i(Y, X))), true2, i(Y, X)) = p(i(Y, X)).
% 189.74/24.56 Proof:
% 189.74/24.56 fresh4(p(i(i(X, Y), i(Y, X))), true2, i(Y, X))
% 189.74/24.56 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.56 fresh3(p(i(i(i(X, Y), i(Y, X)), i(Y, X))), true2, i(i(X, Y), i(Y, X)), i(Y, X))
% 189.74/24.56 = { by axiom 10 (axTO) }
% 189.74/24.56 fresh3(true2, true2, i(i(X, Y), i(Y, X)), i(Y, X))
% 189.74/24.56 = { by axiom 2 (modus_ponens) }
% 189.74/24.56 p(i(Y, X))
% 189.74/24.56
% 189.74/24.56 Lemma 12: fresh4(p(i(X, Y)), true2, i(i(Y, Z), i(X, Z))) = p(i(i(Y, Z), i(X, Z))).
% 189.74/24.56 Proof:
% 189.74/24.56 fresh4(p(i(X, Y)), true2, i(i(Y, Z), i(X, Z)))
% 189.74/24.56 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.56 fresh3(p(i(i(X, Y), i(i(Y, Z), i(X, Z)))), true2, i(X, Y), i(i(Y, Z), i(X, Z)))
% 189.74/24.56 = { by axiom 8 (axBp) }
% 189.74/24.56 fresh3(true2, true2, i(X, Y), i(i(Y, Z), i(X, Z)))
% 189.74/24.56 = { by axiom 2 (modus_ponens) }
% 189.74/24.56 p(i(i(Y, Z), i(X, Z)))
% 189.74/24.56
% 189.74/24.56 Lemma 13: p(i(X, X)) = true2.
% 189.74/24.56 Proof:
% 189.74/24.56 p(i(X, X))
% 189.74/24.56 = { by lemma 11 R->L }
% 189.74/24.56 fresh4(p(i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by lemma 11 R->L }
% 189.74/24.56 fresh4(fresh4(p(i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.56 fresh4(fresh4(fresh3(true2, true2, i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.56 fresh4(fresh4(fresh3(fresh4(true2, true2, i(i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X))))), true2, i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 10 (axTO) R->L }
% 189.74/24.56 fresh4(fresh4(fresh3(fresh4(p(i(i(i(X, X), i(X, X)), i(X, X))), true2, i(i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X))))), true2, i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by lemma 12 }
% 189.74/24.56 fresh4(fresh4(fresh3(p(i(i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X))))), true2, i(i(X, X), i(i(X, X), i(X, X))), i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 5 (modus_ponens) }
% 189.74/24.56 fresh4(fresh4(fresh4(p(i(i(X, X), i(i(X, X), i(X, X)))), true2, i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 8 (axBp) }
% 189.74/24.56 fresh4(fresh4(fresh4(true2, true2, i(i(i(X, X), i(X, X)), i(i(X, X), i(X, X)))), true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 1 (modus_ponens) }
% 189.74/24.56 fresh4(fresh4(true2, true2, i(i(X, X), i(X, X))), true2, i(X, X))
% 189.74/24.56 = { by axiom 1 (modus_ponens) }
% 189.74/24.56 fresh4(true2, true2, i(X, X))
% 189.74/24.56 = { by axiom 1 (modus_ponens) }
% 189.74/24.56 true2
% 189.74/24.56
% 189.74/24.56 Lemma 14: p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))) = true2.
% 189.74/24.56 Proof:
% 189.74/24.56 p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 189.74/24.57 = { by lemma 12 R->L }
% 189.74/24.57 fresh4(p(i(f(i(X, W), i(W, Y)), i(X, Y))), true2, i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 189.74/24.57 = { by axiom 6 (resid2) R->L }
% 189.74/24.57 fresh4(fresh(p(i(i(X, W), i(i(W, Y), i(X, Y)))), true2, i(X, W), i(W, Y), i(X, Y)), true2, i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 189.74/24.57 = { by axiom 8 (axBp) }
% 189.74/24.57 fresh4(fresh(true2, true2, i(X, W), i(W, Y), i(X, Y)), true2, i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 189.74/24.57 = { by axiom 3 (resid2) }
% 189.74/24.57 fresh4(true2, true2, i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 true2
% 189.74/24.57
% 189.74/24.57 Lemma 15: p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))) = true2.
% 189.74/24.57 Proof:
% 189.74/24.57 p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X))))
% 189.74/24.57 = { by axiom 7 (resid1) R->L }
% 189.74/24.57 fresh2(p(i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.57 fresh2(fresh3(true2, true2, i(i(i(X, Y), i(Y, X)), i(Y, X)), i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by lemma 14 R->L }
% 189.74/24.57 fresh2(fresh3(p(i(i(i(i(X, Y), i(Y, X)), i(Y, X)), i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X)))), true2, i(i(i(X, Y), i(Y, X)), i(Y, X)), i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by axiom 5 (modus_ponens) }
% 189.74/24.57 fresh2(fresh4(p(i(i(i(X, Y), i(Y, X)), i(Y, X))), true2, i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by axiom 10 (axTO) }
% 189.74/24.57 fresh2(fresh4(true2, true2, i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 fresh2(true2, true2, i(i(X, Y), Z), i(Z, i(Y, X)), i(Y, X))
% 189.74/24.57 = { by axiom 4 (resid1) }
% 189.74/24.57 true2
% 189.74/24.57
% 189.74/24.57 Lemma 16: p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))) = true2.
% 189.74/24.57 Proof:
% 189.74/24.57 p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W)))
% 189.74/24.57 = { by lemma 12 R->L }
% 189.74/24.57 fresh4(p(i(i(Z, X), i(i(X, Y), i(Z, Y)))), true2, i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W)))
% 189.74/24.57 = { by axiom 8 (axBp) }
% 189.74/24.57 fresh4(true2, true2, i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 true2
% 189.74/24.57
% 189.74/24.57 Lemma 17: fresh4(p(i(i(i(X, Y), i(Z, Y)), W)), true2, i(i(Z, X), W)) = p(i(i(Z, X), W)).
% 189.74/24.57 Proof:
% 189.74/24.57 fresh4(p(i(i(i(X, Y), i(Z, Y)), W)), true2, i(i(Z, X), W))
% 189.74/24.57 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.57 fresh3(p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))), true2, i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))
% 189.74/24.57 = { by lemma 16 }
% 189.74/24.57 fresh3(true2, true2, i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))
% 189.74/24.57 = { by axiom 2 (modus_ponens) }
% 189.74/24.57 p(i(i(Z, X), W))
% 189.74/24.57
% 189.74/24.57 Lemma 18: p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z))) = true2.
% 189.74/24.57 Proof:
% 189.74/24.57 p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z)))
% 189.74/24.57 = { by lemma 12 R->L }
% 189.74/24.57 fresh4(p(i(i(i(Y, X), X), i(i(X, Y), Y))), true2, i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z)))
% 189.74/24.57 = { by axiom 9 (axL) }
% 189.74/24.57 fresh4(true2, true2, i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 true2
% 189.74/24.57
% 189.74/24.57 Lemma 19: fresh4(p(i(X, i(Y, Z))), true2, i(i(i(Z, Y), Y), i(X, Z))) = p(i(i(i(Z, Y), Y), i(X, Z))).
% 189.74/24.57 Proof:
% 189.74/24.57 fresh4(p(i(X, i(Y, Z))), true2, i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.57 fresh3(p(i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true2, i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57 = { by lemma 17 R->L }
% 189.74/24.57 fresh3(fresh4(p(i(i(i(i(Y, Z), Z), i(X, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true2, i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true2, i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57 = { by lemma 18 }
% 189.74/24.57 fresh3(fresh4(true2, true2, i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true2, i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 fresh3(true2, true2, i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57 = { by axiom 2 (modus_ponens) }
% 189.74/24.57 p(i(i(i(Z, Y), Y), i(X, Z)))
% 189.74/24.57
% 189.74/24.57 Lemma 20: fresh4(p(i(i(X, Y), Y)), true2, i(i(Y, X), X)) = p(i(i(Y, X), X)).
% 189.74/24.57 Proof:
% 189.74/24.57 fresh4(p(i(i(X, Y), Y)), true2, i(i(Y, X), X))
% 189.74/24.57 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.57 fresh3(p(i(i(i(X, Y), Y), i(i(Y, X), X))), true2, i(i(X, Y), Y), i(i(Y, X), X))
% 189.74/24.57 = { by axiom 9 (axL) }
% 189.74/24.57 fresh3(true2, true2, i(i(X, Y), Y), i(i(Y, X), X))
% 189.74/24.57 = { by axiom 2 (modus_ponens) }
% 189.74/24.57 p(i(i(Y, X), X))
% 189.74/24.57
% 189.74/24.57 Lemma 21: p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))) = true2.
% 189.74/24.57 Proof:
% 189.74/24.57 p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z)))))
% 189.74/24.57 = { by lemma 17 R->L }
% 189.74/24.57 fresh4(p(i(i(i(i(Y, Z), i(W, Z)), i(X, i(W, Z))), i(i(W, Y), i(X, i(W, Z))))), true2, i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z)))))
% 189.74/24.57 = { by lemma 16 }
% 189.74/24.57 fresh4(true2, true2, i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z)))))
% 189.74/24.57 = { by axiom 1 (modus_ponens) }
% 189.74/24.57 true2
% 189.74/24.57
% 189.74/24.57 Lemma 22: p(i(i(X, i(Y, Y)), i(Y, Y))) = true2.
% 189.74/24.57 Proof:
% 189.74/24.57 p(i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.57 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.57 fresh3(true2, true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.57 fresh3(fresh4(true2, true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.57 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.57 fresh3(fresh4(fresh4(true2, true2, i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.57 = { by lemma 13 R->L }
% 189.74/24.57 fresh3(fresh4(fresh4(p(i(i(Y, Y), i(Y, Y))), true2, i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(fresh3(true2, true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(fresh3(fresh4(true2, true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(fresh3(fresh4(fresh4(true2, true2, i(i(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(fresh3(fresh4(fresh4(fresh4(true2, true2, i(i(X, i(Y, Y)), i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by lemma 15 R->L }
% 189.74/24.58 fresh3(fresh4(fresh3(fresh3(fresh4(fresh4(fresh4(p(i(i(i(i(Y, Y), i(Y, Y)), i(X, i(Y, Y))), i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))))), true2, i(i(X, i(Y, Y)), i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.58 = { by lemma 17 }
% 189.74/24.59 fresh3(fresh4(fresh3(fresh3(fresh4(fresh4(p(i(i(X, i(Y, Y)), i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by lemma 19 }
% 189.74/24.59 fresh3(fresh4(fresh3(fresh3(fresh4(p(i(i(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by lemma 20 }
% 189.74/24.59 fresh3(fresh4(fresh3(fresh3(p(i(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 5 (modus_ponens) }
% 189.74/24.59 fresh3(fresh4(fresh3(fresh4(p(i(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true2, i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by lemma 21 }
% 189.74/24.59 fresh3(fresh4(fresh3(fresh4(true2, true2, i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 1 (modus_ponens) }
% 189.74/24.59 fresh3(fresh4(fresh3(true2, true2, i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 2 (modus_ponens) }
% 189.74/24.59 fresh3(fresh4(p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true2, i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by lemma 12 }
% 189.74/24.59 fresh3(p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true2, i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 5 (modus_ponens) }
% 189.74/24.59 fresh4(p(i(i(i(Y, Y), i(Y, Y)), i(Y, Y))), true2, i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 10 (axTO) }
% 189.74/24.59 fresh4(true2, true2, i(i(X, i(Y, Y)), i(Y, Y)))
% 189.74/24.59 = { by axiom 1 (modus_ponens) }
% 189.74/24.59 true2
% 189.74/24.59
% 189.74/24.59 Lemma 23: p(i(i(i(X, f(Y, X)), Z), i(Y, Z))) = true2.
% 189.74/24.59 Proof:
% 189.74/24.59 p(i(i(i(X, f(Y, X)), Z), i(Y, Z)))
% 189.74/24.59 = { by lemma 12 R->L }
% 189.74/24.59 fresh4(p(i(Y, i(X, f(Y, X)))), true2, i(i(i(X, f(Y, X)), Z), i(Y, Z)))
% 189.74/24.59 = { by axiom 7 (resid1) R->L }
% 189.74/24.59 fresh4(fresh2(p(i(f(Y, X), f(Y, X))), true2, Y, X, f(Y, X)), true2, i(i(i(X, f(Y, X)), Z), i(Y, Z)))
% 189.74/24.59 = { by lemma 13 }
% 189.74/24.59 fresh4(fresh2(true2, true2, Y, X, f(Y, X)), true2, i(i(i(X, f(Y, X)), Z), i(Y, Z)))
% 189.74/24.59 = { by axiom 4 (resid1) }
% 189.74/24.59 fresh4(true2, true2, i(i(i(X, f(Y, X)), Z), i(Y, Z)))
% 189.74/24.59 = { by axiom 1 (modus_ponens) }
% 189.74/24.59 true2
% 189.74/24.59
% 189.74/24.59 Lemma 24: fresh4(p(i(X, i(Y, Z))), true2, i(i(W, Y), i(X, i(W, Z)))) = p(i(i(W, Y), i(X, i(W, Z)))).
% 189.74/24.59 Proof:
% 189.74/24.59 fresh4(p(i(X, i(Y, Z))), true2, i(i(W, Y), i(X, i(W, Z))))
% 189.74/24.59 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.59 fresh3(p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))), true2, i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))
% 189.74/24.59 = { by lemma 21 }
% 189.74/24.59 fresh3(true2, true2, i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))
% 189.74/24.59 = { by axiom 2 (modus_ponens) }
% 189.74/24.59 p(i(i(W, Y), i(X, i(W, Z))))
% 189.74/24.59
% 189.74/24.59 Goal 1 (axK_axC): tuple(p(i(i(X, i(Y, Z)), i(Y, i(X, Z)))), p(i(c1, i(c2, c1)))) = tuple(true2, true2).
% 189.74/24.59 The goal is true when:
% 189.74/24.59 X = i(i(X, X), X)
% 189.74/24.59 Y = i(i(X, X), X)
% 189.74/24.59 Z = Y
% 189.74/24.59
% 189.74/24.59 Proof:
% 189.74/24.59 tuple(p(i(i(i(i(X, X), X), i(i(i(X, X), X), Y)), i(i(i(X, X), X), i(i(i(X, X), X), Y)))), p(i(c1, i(c2, c1))))
% 189.74/24.60 = { by lemma 18 }
% 189.74/24.60 tuple(true2, p(i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh3(true2, true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh3(fresh4(true2, true2, i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh3(fresh4(fresh4(true2, true2, i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1))))), true2, i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by lemma 23 R->L }
% 189.74/24.60 tuple(true2, fresh3(fresh4(fresh4(p(i(i(i(c1, f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(c2, i(i(c2, c1), f(c2, c1))))), true2, i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1))))), true2, i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by lemma 17 }
% 189.74/24.60 tuple(true2, fresh3(fresh4(p(i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1))))), true2, i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh3(fresh3(p(i(i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1)))), i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))), true2, i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1)))), i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by lemma 15 }
% 189.74/24.60 tuple(true2, fresh3(fresh3(true2, true2, i(i(i(c2, c1), c1), i(c2, i(i(c2, c1), f(c2, c1)))), i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 2 (modus_ponens) }
% 189.74/24.60 tuple(true2, fresh3(p(i(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1)))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1))), i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 5 (modus_ponens) }
% 189.74/24.60 tuple(true2, fresh4(p(i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.60 = { by lemma 24 R->L }
% 189.74/24.60 tuple(true2, fresh4(fresh4(p(i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh4(fresh4(fresh3(true2, true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh4(fresh4(fresh3(fresh4(true2, true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.60 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.60 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(true2, true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.61 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.61 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(true2, true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.61 = { by axiom 4 (resid1) R->L }
% 189.74/24.61 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(true2, true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.61 = { by axiom 1 (modus_ponens) R->L }
% 189.74/24.61 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh4(true2, true2, i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.61 = { by lemma 22 R->L }
% 189.74/24.62 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh4(p(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1)))), true2, i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.62 = { by axiom 5 (modus_ponens) R->L }
% 189.74/24.62 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(p(i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 189.74/24.62 = { by axiom 2 (modus_ponens) R->L }
% 189.74/24.62 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(fresh3(true2, true2, i(i(i(i(f(c2, c1), f(c2, c1)), c1), c1), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.63 = { by lemma 18 R->L }
% 191.04/24.63 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(fresh3(p(i(i(i(i(i(f(c2, c1), f(c2, c1)), c1), c1), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)))), true2, i(i(i(i(f(c2, c1), f(c2, c1)), c1), c1), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.63 = { by axiom 5 (modus_ponens) }
% 191.04/24.63 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(fresh4(p(i(i(i(i(f(c2, c1), f(c2, c1)), c1), c1), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.63 = { by lemma 14 }
% 191.04/24.63 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(fresh4(true2, true2, i(i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1))), true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.63 = { by axiom 1 (modus_ponens) }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(fresh3(true2, true2, i(i(c1, i(f(c2, c1), f(c2, c1))), i(f(c2, c1), f(c2, c1))), i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by axiom 2 (modus_ponens) }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(fresh2(p(i(f(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1)), c1)), true2, i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(c2, c1), f(c2, c1)), c1), c1), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by axiom 7 (resid1) }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(fresh4(p(i(i(i(f(c2, c1), f(c2, c1)), i(i(c2, c1), f(c2, c1))), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by lemma 17 }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(fresh4(fresh4(p(i(i(i(c2, c1), f(c2, c1)), i(i(i(i(c2, c1), f(c2, c1)), c1), c1))), true2, i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by lemma 19 }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(fresh4(p(i(i(i(c1, i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1)), i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by lemma 20 }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh3(p(i(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by axiom 5 (modus_ponens) }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh4(p(i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.64 = { by lemma 24 R->L }
% 191.04/24.64 tuple(true2, fresh4(fresh4(fresh4(fresh4(p(i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 2 (modus_ponens) R->L }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh3(true2, true2, i(i(c1, f(c1, c1)), i(c1, c1)), i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by lemma 23 R->L }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh3(p(i(i(i(c1, f(c1, c1)), i(c1, c1)), i(c1, i(c1, c1)))), true2, i(i(c1, f(c1, c1)), i(c1, c1)), i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 5 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh4(p(i(i(c1, f(c1, c1)), i(c1, c1))), true2, i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by lemma 17 R->L }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh4(fresh4(p(i(i(i(f(c1, c1), c1), i(c1, c1)), i(c1, c1))), true2, i(i(c1, f(c1, c1)), i(c1, c1))), true2, i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by lemma 22 }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh4(fresh4(true2, true2, i(i(c1, f(c1, c1)), i(c1, c1))), true2, i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(fresh4(true2, true2, i(c1, i(c1, c1))), true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(fresh4(true2, true2, i(i(i(i(c2, c1), f(c2, c1)), c1), i(c1, i(i(i(c2, c1), f(c2, c1)), c1)))), true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(fresh4(fresh4(true2, true2, i(c1, i(i(i(c2, c1), f(c2, c1)), c1))), true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(fresh4(true2, true2, i(i(c2, i(i(c2, c1), f(c2, c1))), i(c1, i(c2, c1)))), true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, fresh4(true2, true2, i(c1, i(c2, c1))))
% 191.04/24.65 = { by axiom 1 (modus_ponens) }
% 191.04/24.65 tuple(true2, true2)
% 191.04/24.65 % SZS output end Proof
% 191.04/24.65
% 191.04/24.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------