TSTP Solution File: CAT002-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CAT002-3 : 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 : n019.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 18:18:48 EDT 2023
% Result : Unsatisfiable 0.21s 0.44s
% 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 : CAT002-3 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14 % 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 : n019.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 00:30:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.44 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Take the following subset of the input axioms:
% 0.21/0.45 fof(ab_h_equals_ab_g, hypothesis, compose(compose(a, b), h)=compose(compose(a, b), g)).
% 0.21/0.45 fof(associativity_of_compose, axiom, ![X, Y, Z]: compose(X, compose(Y, Z))=compose(compose(X, Y), Z)).
% 0.21/0.45 fof(cancellation_for_compose1, hypothesis, ![X2, Y2, Z2]: (compose(a, X2)!=Y2 | (compose(a, Z2)!=Y2 | X2=Z2))).
% 0.21/0.45 fof(cancellation_for_compose2, hypothesis, ![X2, Y2, Z2]: (compose(b, X2)!=Y2 | (compose(b, Z2)!=Y2 | X2=Z2))).
% 0.21/0.45 fof(prove_g_equals_h, negated_conjecture, g!=h).
% 0.21/0.45
% 0.21/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.45 fresh(y, y, x1...xn) = u
% 0.21/0.45 C => fresh(s, t, x1...xn) = v
% 0.21/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.45 variables of u and v.
% 0.21/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.45 input problem has no model of domain size 1).
% 0.21/0.45
% 0.21/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.45
% 0.21/0.45 Axiom 1 (associativity_of_compose): compose(X, compose(Y, Z)) = compose(compose(X, Y), Z).
% 0.21/0.45 Axiom 2 (ab_h_equals_ab_g): compose(compose(a, b), h) = compose(compose(a, b), g).
% 0.21/0.45 Axiom 3 (cancellation_for_compose1): fresh4(X, X, Y, Z) = Z.
% 0.21/0.45 Axiom 4 (cancellation_for_compose2): fresh2(X, X, Y, Z) = Z.
% 0.21/0.45 Axiom 5 (cancellation_for_compose1): fresh5(X, X, Y, Z, W) = Y.
% 0.21/0.45 Axiom 6 (cancellation_for_compose2): fresh3(X, X, Y, Z, W) = Y.
% 0.21/0.45 Axiom 7 (cancellation_for_compose1): fresh5(compose(a, X), Y, Z, Y, X) = fresh4(compose(a, Z), Y, Z, X).
% 0.21/0.45 Axiom 8 (cancellation_for_compose2): fresh3(compose(b, X), Y, Z, Y, X) = fresh2(compose(b, Z), Y, Z, X).
% 0.21/0.45
% 0.21/0.45 Goal 1 (prove_g_equals_h): g = h.
% 0.21/0.45 Proof:
% 0.21/0.45 g
% 0.21/0.45 = { by axiom 4 (cancellation_for_compose2) R->L }
% 0.21/0.45 fresh2(compose(b, h), compose(b, h), h, g)
% 0.21/0.45 = { by axiom 5 (cancellation_for_compose1) R->L }
% 0.21/0.45 fresh2(compose(b, h), fresh5(compose(a, compose(b, g)), compose(a, compose(b, g)), compose(b, h), compose(a, compose(b, g)), compose(b, g)), h, g)
% 0.21/0.45 = { by axiom 7 (cancellation_for_compose1) }
% 0.21/0.45 fresh2(compose(b, h), fresh4(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), h, g)
% 0.21/0.45 = { by axiom 1 (associativity_of_compose) }
% 0.21/0.45 fresh2(compose(b, h), fresh4(compose(a, compose(b, h)), compose(compose(a, b), g), compose(b, h), compose(b, g)), h, g)
% 0.21/0.45 = { by axiom 2 (ab_h_equals_ab_g) R->L }
% 0.21/0.45 fresh2(compose(b, h), fresh4(compose(a, compose(b, h)), compose(compose(a, b), h), compose(b, h), compose(b, g)), h, g)
% 0.21/0.45 = { by axiom 1 (associativity_of_compose) R->L }
% 0.21/0.45 fresh2(compose(b, h), fresh4(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), h, g)
% 0.21/0.45 = { by axiom 3 (cancellation_for_compose1) }
% 0.21/0.45 fresh2(compose(b, h), compose(b, g), h, g)
% 0.21/0.45 = { by axiom 8 (cancellation_for_compose2) R->L }
% 0.21/0.45 fresh3(compose(b, g), compose(b, g), h, compose(b, g), g)
% 0.21/0.45 = { by axiom 6 (cancellation_for_compose2) }
% 0.21/0.45 h
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45
% 0.21/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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