TSTP Solution File: CAT001-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT001-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : Wed Aug 30 18:18:47 EDT 2023
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CAT001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 00:03:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.21/0.42 % SZS status Unsatisfiable
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% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Take the following subset of the input axioms:
% 0.21/0.42 fof(associativity_of_compose, axiom, ![X, Y, Z]: compose(X, compose(Y, Z))=compose(compose(X, Y), Z)).
% 0.21/0.42 fof(bh_equals_bg, hypothesis, compose(b, h)=compose(b, g)).
% 0.21/0.42 fof(monomorphism, hypothesis, ![X2, Y2, Z2]: (compose(compose(a, b), X2)!=Y2 | (compose(compose(a, b), Z2)!=Y2 | X2=Z2))).
% 0.21/0.42 fof(prove_h_equals_g, negated_conjecture, h!=g).
% 0.21/0.42
% 0.21/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.42 fresh(y, y, x1...xn) = u
% 0.21/0.42 C => fresh(s, t, x1...xn) = v
% 0.21/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.42 variables of u and v.
% 0.21/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.42 input problem has no model of domain size 1).
% 0.21/0.42
% 0.21/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.42
% 0.21/0.42 Axiom 1 (bh_equals_bg): compose(b, h) = compose(b, g).
% 0.21/0.42 Axiom 2 (associativity_of_compose): compose(X, compose(Y, Z)) = compose(compose(X, Y), Z).
% 0.21/0.42 Axiom 3 (monomorphism): fresh2(X, X, Y, Z) = Z.
% 0.21/0.42 Axiom 4 (monomorphism): fresh3(X, X, Y, Z, W) = Y.
% 0.21/0.42 Axiom 5 (monomorphism): fresh3(compose(compose(a, b), X), Y, Z, Y, X) = fresh2(compose(compose(a, b), Z), Y, Z, X).
% 0.21/0.42
% 0.21/0.42 Goal 1 (prove_h_equals_g): h = g.
% 0.21/0.42 Proof:
% 0.21/0.42 h
% 0.21/0.42 = { by axiom 4 (monomorphism) R->L }
% 0.21/0.42 fresh3(compose(a, compose(b, g)), compose(a, compose(b, g)), h, compose(a, compose(b, g)), g)
% 0.21/0.42 = { by axiom 2 (associativity_of_compose) }
% 0.21/0.42 fresh3(compose(compose(a, b), g), compose(a, compose(b, g)), h, compose(a, compose(b, g)), g)
% 0.21/0.42 = { by axiom 5 (monomorphism) }
% 0.21/0.42 fresh2(compose(compose(a, b), h), compose(a, compose(b, g)), h, g)
% 0.21/0.42 = { by axiom 2 (associativity_of_compose) R->L }
% 0.21/0.42 fresh2(compose(a, compose(b, h)), compose(a, compose(b, g)), h, g)
% 0.21/0.42 = { by axiom 1 (bh_equals_bg) R->L }
% 0.21/0.42 fresh2(compose(a, compose(b, h)), compose(a, compose(b, h)), h, g)
% 0.21/0.42 = { by axiom 3 (monomorphism) }
% 0.21/0.42 g
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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