TSTP Solution File: COL079-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL079-1 : TPTP v8.1.2. Released v1.2.0.
% 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 : n005.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 : Wed Aug 30 18:32:01 EDT 2023
% Result : Unsatisfiable 76.47s 10.17s
% Output : Proof 76.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL079-1 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Aug 27 04:14:53 EDT 2023
% 0.13/0.36 % CPUTime :
% 76.47/10.17 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 76.47/10.17
% 76.47/10.17 % SZS status Unsatisfiable
% 76.47/10.17
% 76.47/10.18 % SZS output start Proof
% 76.47/10.18 Take the following subset of the input axioms:
% 76.47/10.18 fof(abstraction, axiom, ![X, Y, Z]: apply(apply(apply(abstraction, X), Y), Z)=apply(apply(X, k(Z)), apply(Y, Z))).
% 76.47/10.18 fof(extensionality2, axiom, ![X2, Y2]: (X2=Y2 | apply(X2, n(X2, Y2))!=apply(Y2, n(X2, Y2)))).
% 76.47/10.18 fof(k_definition, axiom, ![X2, Y2]: apply(k(X2), Y2)=X2).
% 76.47/10.18 fof(pairing, axiom, ![X2]: pair(apply(projection1, X2), apply(projection2, X2))=X2).
% 76.47/10.18 fof(pairwise_application, axiom, ![X2, Y2, Z2]: apply(pair(X2, Y2), Z2)=pair(apply(X2, Z2), apply(Y2, Z2))).
% 76.47/10.18 fof(projection2, axiom, ![X2, Y2]: apply(projection2, pair(X2, Y2))=Y2).
% 76.47/10.18 fof(prove_TRC2a, negated_conjecture, apply(abstraction, apply(abstraction, apply(abstraction, b)))!=apply(abstraction, b)).
% 76.47/10.18
% 76.47/10.18 Now clausify the problem and encode Horn clauses using encoding 3 of
% 76.47/10.18 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 76.47/10.18 We repeatedly replace C & s=t => u=v by the two clauses:
% 76.47/10.18 fresh(y, y, x1...xn) = u
% 76.47/10.18 C => fresh(s, t, x1...xn) = v
% 76.47/10.18 where fresh is a fresh function symbol and x1..xn are the free
% 76.47/10.18 variables of u and v.
% 76.47/10.18 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 76.47/10.18 input problem has no model of domain size 1).
% 76.47/10.18
% 76.47/10.18 The encoding turns the above axioms into the following unit equations and goals:
% 76.47/10.18
% 76.47/10.18 Axiom 1 (k_definition): apply(k(X), Y) = X.
% 76.47/10.18 Axiom 2 (projection2): apply(projection2, pair(X, Y)) = Y.
% 76.47/10.18 Axiom 3 (extensionality2): fresh(X, X, Y, Z) = Z.
% 76.47/10.18 Axiom 4 (pairwise_application): apply(pair(X, Y), Z) = pair(apply(X, Z), apply(Y, Z)).
% 76.47/10.18 Axiom 5 (pairing): pair(apply(projection1, X), apply(projection2, X)) = X.
% 76.47/10.18 Axiom 6 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, k(Z)), apply(Y, Z)).
% 76.47/10.18 Axiom 7 (extensionality2): fresh(apply(X, n(X, Y)), apply(Y, n(X, Y)), X, Y) = X.
% 76.47/10.18
% 76.47/10.18 Lemma 8: apply(projection2, apply(pair(X, Y), Z)) = apply(Y, Z).
% 76.47/10.18 Proof:
% 76.47/10.18 apply(projection2, apply(pair(X, Y), Z))
% 76.47/10.18 = { by axiom 4 (pairwise_application) }
% 76.47/10.18 apply(projection2, pair(apply(X, Z), apply(Y, Z)))
% 76.47/10.18 = { by axiom 2 (projection2) }
% 76.47/10.18 apply(Y, Z)
% 76.47/10.18
% 76.47/10.18 Lemma 9: apply(apply(apply(abstraction, X), k(Y)), Z) = apply(apply(X, k(Z)), Y).
% 76.47/10.18 Proof:
% 76.47/10.18 apply(apply(apply(abstraction, X), k(Y)), Z)
% 76.47/10.18 = { by axiom 6 (abstraction) }
% 76.47/10.18 apply(apply(X, k(Z)), apply(k(Y), Z))
% 76.47/10.18 = { by axiom 1 (k_definition) }
% 76.47/10.19 apply(apply(X, k(Z)), Y)
% 76.47/10.19
% 76.47/10.19 Goal 1 (prove_TRC2a): apply(abstraction, apply(abstraction, apply(abstraction, b))) = apply(abstraction, b).
% 76.47/10.19 Proof:
% 76.47/10.19 apply(abstraction, apply(abstraction, apply(abstraction, b)))
% 76.47/10.19 = { by axiom 7 (extensionality2) R->L }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by lemma 8 R->L }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, apply(pair(apply(projection1, apply(pair(apply(abstraction, k(X)), abstraction), b)), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 5 (pairing) }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, apply(apply(pair(apply(abstraction, k(X)), abstraction), b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 4 (pairwise_application) }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, apply(pair(apply(apply(abstraction, k(X)), b), apply(abstraction, b)), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 4 (pairwise_application) }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(apply(apply(abstraction, k(X)), b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 6 (abstraction) }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(apply(k(X), k(n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 1 (k_definition) }
% 76.47/10.19 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.19 = { by axiom 3 (extensionality2) R->L }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), fresh(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by axiom 6 (abstraction) }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), fresh(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(apply(abstraction, apply(abstraction, b)), k(n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by lemma 9 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), fresh(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(apply(abstraction, b), k(apply(n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by lemma 9 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), fresh(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(b, k(n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by axiom 6 (abstraction) R->L }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), fresh(apply(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), n(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(apply(abstraction, b), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by axiom 7 (extensionality2) }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))
% 76.47/10.20 = { by lemma 8 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))
% 76.47/10.20 = { by lemma 8 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b))))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))
% 76.47/10.20 = { by lemma 8 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(projection2, apply(pair(apply(abstraction, k(X)), abstraction), b)))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b)))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))
% 76.47/10.20 = { by lemma 8 }
% 76.47/10.20 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))), apply(projection2, pair(apply(X, apply(b, n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b)))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))
% 76.47/10.20 = { by axiom 2 (projection2) }
% 76.47/10.21 fresh(apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))), apply(apply(abstraction, apply(abstraction, apply(abstraction, b))), n(apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))), apply(abstraction, apply(abstraction, apply(abstraction, b))), apply(abstraction, b))
% 76.47/10.21 = { by axiom 3 (extensionality2) }
% 76.47/10.21 apply(abstraction, b)
% 76.47/10.21 % SZS output end Proof
% 76.47/10.21
% 76.47/10.21 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------