TSTP Solution File: LCL927-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL927-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n006.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 143.28s 18.76s
% Output : Proof 144.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : LCL927-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.38 % Computer : n006.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Fri Aug 25 04:35:53 EDT 2023
% 0.16/0.39 % CPUTime :
% 143.28/18.76 Command-line arguments: --no-flatten-goal
% 143.28/18.76
% 143.28/18.76 % SZS status Unsatisfiable
% 143.28/18.76
% 144.00/18.87 % SZS output start Proof
% 144.00/18.87 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 144.00/18.87 Axiom 2 (axBp): p(i(i(X, Y), i(i(Y, Z), i(X, Z)))) = true.
% 144.00/18.87 Axiom 3 (axL): p(i(i(i(X, Y), Y), i(i(Y, X), X))) = true.
% 144.00/18.87 Axiom 4 (axTO): p(i(i(i(X, Y), i(Y, X)), i(Y, X))) = true.
% 144.00/18.87 Axiom 5 (modus_ponens): ifeq(p(i(X, Y)), true, ifeq(p(X), true, p(Y), true), true) = true.
% 144.00/18.87 Axiom 6 (resid2): ifeq(p(i(X, i(Y, Z))), true, p(i(f(X, Y), Z)), true) = true.
% 144.00/18.87 Axiom 7 (resid1): ifeq(p(i(f(X, Y), Z)), true, p(i(X, i(Y, Z))), true) = true.
% 144.00/18.87
% 144.00/18.87 Lemma 8: ifeq(p(i(i(i(i(X, Y), i(Y, X)), i(Y, X)), Z)), true, p(Z), true) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 ifeq(p(i(i(i(i(X, Y), i(Y, X)), i(Y, X)), Z)), true, p(Z), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(p(i(i(i(i(X, Y), i(Y, X)), i(Y, X)), Z)), true, ifeq(true, true, p(Z), true), true)
% 144.00/18.87 = { by axiom 4 (axTO) R->L }
% 144.00/18.87 ifeq(p(i(i(i(i(X, Y), i(Y, X)), i(Y, X)), Z)), true, ifeq(p(i(i(i(X, Y), i(Y, X)), i(Y, X))), true, p(Z), true), true)
% 144.00/18.87 = { by axiom 5 (modus_ponens) }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 9: ifeq(p(i(X, Y)), true, p(i(i(Y, Z), i(X, Z))), true) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 ifeq(p(i(X, Y)), true, p(i(i(Y, Z), i(X, Z))), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, ifeq(p(i(X, Y)), true, p(i(i(Y, Z), i(X, Z))), true), true)
% 144.00/18.87 = { by axiom 2 (axBp) R->L }
% 144.00/18.87 ifeq(p(i(i(X, Y), i(i(Y, Z), i(X, Z)))), true, ifeq(p(i(X, Y)), true, p(i(i(Y, Z), i(X, Z))), true), true)
% 144.00/18.87 = { by axiom 5 (modus_ponens) }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 10: p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W)))
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))), true)
% 144.00/18.87 = { by axiom 2 (axBp) R->L }
% 144.00/18.87 ifeq(p(i(i(Z, X), i(i(X, Y), i(Z, Y)))), true, p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))), true)
% 144.00/18.87 = { by lemma 9 }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 11: p(i(X, X)) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 p(i(X, X))
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, p(i(X, X)), true)
% 144.00/18.87 = { by lemma 8 R->L }
% 144.00/18.87 ifeq(ifeq(p(i(i(i(i(X, X), i(X, X)), i(X, X)), i(i(X, X), i(X, X)))), true, p(i(i(X, X), i(X, X))), true), true, p(i(X, X)), true)
% 144.00/18.87 = { by lemma 10 }
% 144.00/18.87 ifeq(ifeq(true, true, p(i(i(X, X), i(X, X))), true), true, p(i(X, X)), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) }
% 144.00/18.87 ifeq(p(i(i(X, X), i(X, X))), true, p(i(X, X)), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, ifeq(p(i(i(X, X), i(X, X))), true, p(i(X, X)), true), true)
% 144.00/18.87 = { by axiom 4 (axTO) R->L }
% 144.00/18.87 ifeq(p(i(i(i(X, X), i(X, X)), i(X, X))), true, ifeq(p(i(i(X, X), i(X, X))), true, p(i(X, X)), true), true)
% 144.00/18.87 = { by axiom 5 (modus_ponens) }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 12: ifeq(p(i(i(i(X, Y), i(Z, Y)), W)), true, p(i(i(Z, X), W)), true) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 ifeq(p(i(i(i(X, Y), i(Z, Y)), W)), true, p(i(i(Z, X), W)), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, ifeq(p(i(i(i(X, Y), i(Z, Y)), W)), true, p(i(i(Z, X), W)), true), true)
% 144.00/18.87 = { by lemma 10 R->L }
% 144.00/18.87 ifeq(p(i(i(i(i(X, Y), i(Z, Y)), W), i(i(Z, X), W))), true, ifeq(p(i(i(i(X, Y), i(Z, Y)), W)), true, p(i(i(Z, X), W)), true), true)
% 144.00/18.87 = { by axiom 5 (modus_ponens) }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 13: p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z))) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z)))
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z))), true)
% 144.00/18.87 = { by axiom 3 (axL) R->L }
% 144.00/18.87 ifeq(p(i(i(i(Y, X), X), i(i(X, Y), Y))), true, p(i(i(i(i(X, Y), Y), Z), i(i(i(Y, X), X), Z))), true)
% 144.00/18.87 = { by lemma 9 }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 14: ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true), true)
% 144.00/18.87 = { by lemma 12 R->L }
% 144.00/18.87 ifeq(ifeq(p(i(i(i(i(Y, Z), Z), i(X, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true, p(i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true), true)
% 144.00/18.87 = { by lemma 13 }
% 144.00/18.87 ifeq(ifeq(true, true, p(i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) }
% 144.00/18.87 ifeq(p(i(i(X, i(Y, Z)), i(i(i(Z, Y), Y), i(X, Z)))), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(i(Z, Y), Y), i(X, Z))), true), true)
% 144.00/18.87 = { by axiom 5 (modus_ponens) }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 15: p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z)))
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.87 ifeq(true, true, p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))), true)
% 144.00/18.87 = { by axiom 6 (resid2) R->L }
% 144.00/18.87 ifeq(ifeq(p(i(i(X, W), i(i(W, Y), i(X, Y)))), true, p(i(f(i(X, W), i(W, Y)), i(X, Y))), true), true, p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))), true)
% 144.00/18.87 = { by axiom 2 (axBp) }
% 144.00/18.87 ifeq(ifeq(true, true, p(i(f(i(X, W), i(W, Y)), i(X, Y))), true), true, p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))), true)
% 144.00/18.87 = { by axiom 1 (ifeq_axiom) }
% 144.00/18.87 ifeq(p(i(f(i(X, W), i(W, Y)), i(X, Y))), true, p(i(i(i(X, Y), Z), i(f(i(X, W), i(W, Y)), Z))), true)
% 144.00/18.87 = { by lemma 9 }
% 144.00/18.87 true
% 144.00/18.87
% 144.00/18.87 Lemma 16: p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))) = true.
% 144.00/18.87 Proof:
% 144.00/18.87 p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X))))
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.88 ifeq(true, true, p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))), true)
% 144.00/18.88 = { by lemma 8 R->L }
% 144.00/18.88 ifeq(ifeq(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)))), true, p(i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true), true, p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))), true)
% 144.00/18.88 = { by lemma 15 }
% 144.00/18.88 ifeq(ifeq(true, true, p(i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true), true, p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))), true)
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) }
% 144.00/18.88 ifeq(p(i(f(i(i(X, Y), Z), i(Z, i(Y, X))), i(Y, X))), true, p(i(i(i(X, Y), Z), i(i(Z, i(Y, X)), i(Y, X)))), true)
% 144.00/18.88 = { by axiom 7 (resid1) }
% 144.00/18.88 true
% 144.00/18.88
% 144.00/18.88 Lemma 17: ifeq(p(i(i(X, Y), Y)), true, p(i(i(Y, X), X)), true) = true.
% 144.00/18.88 Proof:
% 144.00/18.88 ifeq(p(i(i(X, Y), Y)), true, p(i(i(Y, X), X)), true)
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.88 ifeq(true, true, ifeq(p(i(i(X, Y), Y)), true, p(i(i(Y, X), X)), true), true)
% 144.00/18.88 = { by axiom 3 (axL) R->L }
% 144.00/18.88 ifeq(p(i(i(i(X, Y), Y), i(i(Y, X), X))), true, ifeq(p(i(i(X, Y), Y)), true, p(i(i(Y, X), X)), true), true)
% 144.00/18.88 = { by axiom 5 (modus_ponens) }
% 144.00/18.88 true
% 144.00/18.88
% 144.00/18.88 Lemma 18: p(i(i(X, i(Y, Y)), i(Y, Y))) = true.
% 144.00/18.88 Proof:
% 144.00/18.88 p(i(i(X, i(Y, Y)), i(Y, Y)))
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.88 ifeq(true, true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by lemma 9 R->L }
% 144.00/18.88 ifeq(ifeq(p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.88 ifeq(ifeq(ifeq(true, true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by lemma 11 R->L }
% 144.00/18.88 ifeq(ifeq(ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.88 ifeq(ifeq(ifeq(true, true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by axiom 5 (modus_ponens) R->L }
% 144.00/18.88 ifeq(ifeq(ifeq(ifeq(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)))))), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 144.00/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.00/18.89 = { by lemma 14 R->L }
% 144.63/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(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))))), true, 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))))), true), true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.89 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, 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))))), true), true, 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))))), true), true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.89 = { by lemma 16 R->L }
% 144.63/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(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))))), true, 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))))), true), true, 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))))), true), true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.89 = { by lemma 12 }
% 144.63/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, 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))))), true), true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.89 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.90 ifeq(ifeq(ifeq(ifeq(ifeq(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))))), true, 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)))))), true), true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.90 = { by lemma 17 }
% 144.63/18.90 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.90 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.90 ifeq(ifeq(ifeq(ifeq(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)))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.90 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.90 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.90 = { by lemma 9 R->L }
% 144.63/18.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.90 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.91 = { by axiom 5 (modus_ponens) R->L }
% 144.63/18.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true, ifeq(p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.91 = { by axiom 2 (axBp) }
% 144.63/18.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true, ifeq(true, true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.91 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.92 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.92 = { by lemma 9 R->L }
% 144.63/18.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))))), true, p(i(i(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.92 = { by lemma 16 }
% 144.63/18.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.92 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))), i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by lemma 12 }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(i(Y, Y), i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by lemma 12 }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(i(Y, Y), 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(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))))), true, 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)))))), true), true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by lemma 12 }
% 144.63/18.93 ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(ifeq(ifeq(p(i(i(i(Y, Y), i(Y, Y)), i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y))))), true, ifeq(p(i(i(Y, Y), i(Y, Y))), true, p(i(i(X, i(Y, Y)), i(i(Y, Y), i(Y, Y)))), true), true), true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by axiom 5 (modus_ponens) }
% 144.63/18.93 ifeq(ifeq(true, true, p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(p(i(i(i(i(Y, Y), i(Y, Y)), i(Y, Y)), i(i(X, i(Y, Y)), i(Y, Y)))), true, p(i(i(X, i(Y, Y)), i(Y, Y))), true)
% 144.63/18.93 = { by lemma 8 }
% 144.63/18.93 true
% 144.63/18.93
% 144.63/18.93 Lemma 19: p(i(X, i(Y, Y))) = true.
% 144.63/18.93 Proof:
% 144.63/18.93 p(i(X, i(Y, Y)))
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.93 ifeq(true, true, p(i(X, i(Y, Y))), true)
% 144.63/18.93 = { by lemma 12 R->L }
% 144.63/18.93 ifeq(ifeq(p(i(i(i(f(X, Y), Y), i(Y, Y)), i(Y, Y))), true, p(i(i(Y, f(X, Y)), i(Y, Y))), true), true, p(i(X, i(Y, Y))), true)
% 144.63/18.93 = { by lemma 18 }
% 144.63/18.93 ifeq(ifeq(true, true, p(i(i(Y, f(X, Y)), i(Y, Y))), true), true, p(i(X, i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.93 ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true)
% 144.63/18.93 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.93 ifeq(true, true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by lemma 9 R->L }
% 144.63/18.94 ifeq(ifeq(p(i(X, i(Y, f(X, Y)))), true, p(i(i(i(Y, f(X, Y)), i(Y, Y)), i(X, i(Y, Y)))), true), true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 ifeq(ifeq(ifeq(true, true, p(i(X, i(Y, f(X, Y)))), true), true, p(i(i(i(Y, f(X, Y)), i(Y, Y)), i(X, i(Y, Y)))), true), true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by lemma 11 R->L }
% 144.63/18.94 ifeq(ifeq(ifeq(p(i(f(X, Y), f(X, Y))), true, p(i(X, i(Y, f(X, Y)))), true), true, p(i(i(i(Y, f(X, Y)), i(Y, Y)), i(X, i(Y, Y)))), true), true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by axiom 7 (resid1) }
% 144.63/18.94 ifeq(ifeq(true, true, p(i(i(i(Y, f(X, Y)), i(Y, Y)), i(X, i(Y, Y)))), true), true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.94 ifeq(p(i(i(i(Y, f(X, Y)), i(Y, Y)), i(X, i(Y, Y)))), true, ifeq(p(i(i(Y, f(X, Y)), i(Y, Y))), true, p(i(X, i(Y, Y))), true), true)
% 144.63/18.94 = { by axiom 5 (modus_ponens) }
% 144.63/18.94 true
% 144.63/18.94
% 144.63/18.94 Lemma 20: ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true) = true.
% 144.63/18.94 Proof:
% 144.63/18.94 ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true)
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 ifeq(true, true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true), true)
% 144.63/18.94 = { by lemma 12 R->L }
% 144.63/18.94 ifeq(ifeq(p(i(i(i(i(Y, Z), i(W, Z)), i(X, i(W, Z))), i(i(W, Y), i(X, i(W, Z))))), true, p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))), true), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true), true)
% 144.63/18.94 = { by lemma 10 }
% 144.63/18.94 ifeq(ifeq(true, true, p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))), true), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true), true)
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.94 ifeq(p(i(i(X, i(Y, Z)), i(i(W, Y), i(X, i(W, Z))))), true, ifeq(p(i(X, i(Y, Z))), true, p(i(i(W, Y), i(X, i(W, Z)))), true), true)
% 144.63/18.94 = { by axiom 5 (modus_ponens) }
% 144.63/18.94 true
% 144.63/18.94
% 144.63/18.94 Goal 1 (axK_axC): tuple(p(i(i(X, i(Y, Z)), i(Y, i(X, Z)))), p(i(c1, i(c2, c1)))) = tuple(true, true).
% 144.63/18.94 The goal is true when:
% 144.63/18.94 X = i(i(Y, Y), Y)
% 144.63/18.94 Y = i(i(Y, Y), Y)
% 144.63/18.94 Z = Z
% 144.63/18.94
% 144.63/18.94 Proof:
% 144.63/18.94 tuple(p(i(i(i(i(Y, Y), Y), i(i(i(Y, Y), Y), Z)), i(i(i(Y, Y), Y), i(i(i(Y, Y), Y), Z)))), p(i(c1, i(c2, c1))))
% 144.63/18.94 = { by lemma 13 }
% 144.63/18.94 tuple(true, p(i(c1, i(c2, c1))))
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 tuple(true, ifeq(true, true, p(i(c1, i(c2, c1))), true))
% 144.63/18.94 = { by lemma 19 R->L }
% 144.63/18.94 tuple(true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true))
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 tuple(true, ifeq(true, true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by lemma 20 R->L }
% 144.63/18.94 tuple(true, ifeq(ifeq(p(i(c1, i(i(X, X), c1))), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 tuple(true, ifeq(ifeq(ifeq(true, true, p(i(c1, i(i(X, X), c1))), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by lemma 20 R->L }
% 144.63/18.94 tuple(true, ifeq(ifeq(ifeq(ifeq(p(i(c1, i(c1, c1))), true, p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true), true, p(i(c1, i(i(X, X), c1))), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by lemma 19 }
% 144.63/18.94 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true), true, p(i(c1, i(i(X, X), c1))), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.94 tuple(true, ifeq(ifeq(ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.94 tuple(true, ifeq(ifeq(ifeq(true, true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by lemma 17 R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by lemma 12 R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by lemma 18 R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.95 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.95 = { by axiom 7 (resid1) R->L }
% 144.63/18.96 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1))), true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.96 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.96 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.96 = { by lemma 15 R->L }
% 144.63/18.96 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), c1), c1)), i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1)))), true, p(i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.96 = { by axiom 1 (ifeq_axiom) R->L }
% 144.63/18.96 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), c1), c1)), i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1)))), true, ifeq(true, true, p(i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.96 = { by axiom 3 (axL) R->L }
% 144.63/18.96 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), c1), c1)), i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1)))), true, ifeq(p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), c1), c1))), true, p(i(f(i(i(c1, i(X, X)), i(X, X)), i(i(X, X), i(X, X))), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.96 = { by axiom 5 (modus_ponens) }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(i(c1, i(X, X)), i(X, X)), i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1)))), true, ifeq(p(i(i(c1, i(X, X)), i(X, X))), true, p(i(i(i(X, X), i(X, X)), i(i(i(X, X), c1), c1))), true), true), true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 5 (modus_ponens) }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(X, X), i(i(i(X, X), c1), c1))), true), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(p(i(i(X, X), i(i(i(X, X), c1), c1))), true, p(i(i(i(c1, i(i(X, X), c1)), i(i(X, X), c1)), i(i(X, X), c1))), true), true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by lemma 14 }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.97 tuple(true, ifeq(ifeq(ifeq(p(i(i(i(i(X, X), c1), i(c1, i(i(X, X), c1))), i(c1, i(i(X, X), c1)))), true, ifeq(p(i(i(i(X, X), c1), i(c1, i(i(X, X), c1)))), true, p(i(c1, i(i(X, X), c1))), true), true), true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 5 (modus_ponens) }
% 144.63/18.97 tuple(true, ifeq(ifeq(true, true, p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 1 (ifeq_axiom) }
% 144.63/18.97 tuple(true, ifeq(p(i(i(c2, i(X, X)), i(c1, i(c2, c1)))), true, ifeq(p(i(c2, i(X, X))), true, p(i(c1, i(c2, c1))), true), true))
% 144.63/18.97 = { by axiom 5 (modus_ponens) }
% 144.63/18.97 tuple(true, true)
% 144.63/18.97 % SZS output end Proof
% 144.63/18.97
% 144.63/18.97 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------