TSTP Solution File: COL080-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL080-1 : 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 : n016.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 18:32:02 EDT 2023
% Result : Unsatisfiable 19.28s 3.05s
% Output : Proof 19.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL080-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.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 : Sun Aug 27 05:07:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 19.28/3.05 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 19.28/3.05
% 19.28/3.05 % SZS status Unsatisfiable
% 19.28/3.05
% 19.28/3.05 % SZS output start Proof
% 19.28/3.05 Take the following subset of the input axioms:
% 19.28/3.05 fof(abstraction, axiom, ![X, Y, Z]: apply(apply(apply(abstraction, X), Y), Z)=apply(apply(X, k(Z)), apply(Y, Z))).
% 19.28/3.05 fof(extensionality2, axiom, ![X2, Y2]: (X2=Y2 | apply(X2, n(X2, Y2))!=apply(Y2, n(X2, Y2)))).
% 19.28/3.05 fof(k_definition, axiom, ![X2, Y2]: apply(k(X2), Y2)=X2).
% 19.28/3.05 fof(prove_TRC2b, negated_conjecture, k(b)!=apply(abstraction, apply(abstraction, k(b)))).
% 19.28/3.05
% 19.28/3.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.28/3.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.28/3.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.28/3.05 fresh(y, y, x1...xn) = u
% 19.28/3.05 C => fresh(s, t, x1...xn) = v
% 19.28/3.05 where fresh is a fresh function symbol and x1..xn are the free
% 19.28/3.05 variables of u and v.
% 19.28/3.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.28/3.05 input problem has no model of domain size 1).
% 19.28/3.05
% 19.28/3.05 The encoding turns the above axioms into the following unit equations and goals:
% 19.28/3.05
% 19.28/3.05 Axiom 1 (k_definition): apply(k(X), Y) = X.
% 19.28/3.05 Axiom 2 (extensionality2): fresh(X, X, Y, Z) = Z.
% 19.28/3.05 Axiom 3 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, k(Z)), apply(Y, Z)).
% 19.28/3.05 Axiom 4 (extensionality2): fresh(apply(X, n(X, Y)), apply(Y, n(X, Y)), X, Y) = X.
% 19.28/3.05
% 19.28/3.05 Goal 1 (prove_TRC2b): k(b) = apply(abstraction, apply(abstraction, k(b))).
% 19.28/3.05 Proof:
% 19.28/3.05 k(b)
% 19.28/3.05 = { by axiom 2 (extensionality2) R->L }
% 19.28/3.05 fresh(b, b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 4 (extensionality2) R->L }
% 19.28/3.05 fresh(fresh(apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))), n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 3 (abstraction) }
% 19.28/3.05 fresh(fresh(apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(apply(apply(abstraction, k(b)), k(n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))))), apply(n(apply(abstraction, apply(abstraction, k(b))), k(b)), n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))))), b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 3 (abstraction) }
% 19.28/3.05 fresh(fresh(apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(apply(k(b), k(apply(n(apply(abstraction, apply(abstraction, k(b))), k(b)), n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))))), apply(k(n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(n(apply(abstraction, apply(abstraction, k(b))), k(b)), n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))))), b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 1 (k_definition) }
% 19.28/3.05 fresh(fresh(apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(b, apply(k(n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(n(apply(abstraction, apply(abstraction, k(b))), k(b)), n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))))), b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 1 (k_definition) }
% 19.28/3.05 fresh(fresh(apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), apply(b, n(b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))))), b, apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b)))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 2 (extensionality2) }
% 19.28/3.05 fresh(apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))), b, apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 1 (k_definition) R->L }
% 19.28/3.05 fresh(apply(apply(abstraction, apply(abstraction, k(b))), n(apply(abstraction, apply(abstraction, k(b))), k(b))), apply(k(b), n(apply(abstraction, apply(abstraction, k(b))), k(b))), apply(abstraction, apply(abstraction, k(b))), k(b))
% 19.28/3.05 = { by axiom 4 (extensionality2) }
% 19.28/3.05 apply(abstraction, apply(abstraction, k(b)))
% 19.28/3.05 % SZS output end Proof
% 19.28/3.05
% 19.28/3.05 RESULT: Unsatisfiable (the axioms are contradictory).
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