TSTP Solution File: COL075-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL075-1 : 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 : n012.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 18:32:00 EDT 2023
% Result : Unsatisfiable 2.16s 0.85s
% Output : Proof 2.16s
% 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 : COL075-1 : 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 : n012.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 04:49:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.16/0.85 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.16/0.85
% 2.16/0.85 % SZS status Unsatisfiable
% 2.16/0.85
% 2.16/0.86 % SZS output start Proof
% 2.16/0.86 Take the following subset of the input axioms:
% 2.16/0.86 fof(abstraction, axiom, ![X, Y, Z]: apply(apply(apply(abstraction, X), Y), Z)=apply(apply(X, apply(k, Z)), apply(Y, Z))).
% 2.16/0.86 fof(k_definition, axiom, ![Y2, X2]: apply(apply(k, X2), Y2)=X2).
% 2.16/0.86 fof(prove_diagonal_combinator, negated_conjecture, ![Y2]: apply(apply(Y2, b(Y2)), c(Y2))!=apply(b(Y2), b(Y2))).
% 2.16/0.86
% 2.16/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.16/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.16/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.16/0.86 fresh(y, y, x1...xn) = u
% 2.16/0.86 C => fresh(s, t, x1...xn) = v
% 2.16/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 2.16/0.86 variables of u and v.
% 2.16/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.16/0.86 input problem has no model of domain size 1).
% 2.16/0.86
% 2.16/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 2.16/0.86
% 2.16/0.86 Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 2.16/0.86 Axiom 2 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, apply(k, Z)), apply(Y, Z)).
% 2.16/0.86
% 2.16/0.86 Goal 1 (prove_diagonal_combinator): apply(apply(X, b(X)), c(X)) = apply(b(X), b(X)).
% 2.16/0.86 The goal is true when:
% 2.16/0.86 X = apply(apply(abstraction, abstraction), k)
% 2.16/0.86
% 2.16/0.86 Proof:
% 2.16/0.86 apply(apply(apply(apply(abstraction, abstraction), k), b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k)))
% 2.16/0.86 = { by axiom 2 (abstraction) }
% 2.16/0.86 apply(apply(apply(abstraction, apply(k, b(apply(apply(abstraction, abstraction), k)))), apply(k, b(apply(apply(abstraction, abstraction), k)))), c(apply(apply(abstraction, abstraction), k)))
% 2.16/0.86 = { by axiom 2 (abstraction) }
% 2.16/0.86 apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), apply(apply(k, b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k))))
% 2.16/0.86 = { by axiom 1 (k_definition) }
% 2.16/0.86 apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), b(apply(apply(abstraction, abstraction), k)))
% 2.16/0.86 = { by axiom 1 (k_definition) }
% 2.16/0.86 apply(b(apply(apply(abstraction, abstraction), k)), b(apply(apply(abstraction, abstraction), k)))
% 2.16/0.86 % SZS output end Proof
% 2.16/0.86
% 2.16/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
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