TSTP Solution File: SET041-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET041-3 : 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 : Thu Aug 31 15:30:50 EDT 2023
% Result : Unsatisfiable 7.31s 1.40s
% Output : Proof 7.31s
% 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 : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 12:23:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 7.31/1.40 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 7.31/1.40
% 7.31/1.40 % SZS status Unsatisfiable
% 7.31/1.40
% 7.31/1.40 % SZS output start Proof
% 7.31/1.40 Take the following subset of the input axioms:
% 7.31/1.40 fof(a_function, hypothesis, function(a_function)).
% 7.31/1.40 fof(apply_for_composition1, axiom, ![X, Xf, Xg]: (~function(Xf) | (~member(X, domain_of(Xf)) | subset(apply(Xg, apply(Xf, X)), apply(compose(Xg, Xf), X))))).
% 7.31/1.40 fof(apply_for_composition2, axiom, ![Xf2, X2, Xg2]: (~function(Xf2) | subset(apply(compose(Xg2, Xf2), X2), apply(Xg2, apply(Xf2, X2))))).
% 7.31/1.40 fof(member_of_domain, hypothesis, member(a, domain_of(a_function))).
% 7.31/1.40 fof(prove_apply_for_composition3, negated_conjecture, apply(another_function, apply(a_function, a))!=apply(compose(another_function, a_function), a)).
% 7.31/1.40 fof(two_sets_equal, axiom, ![Y, X2]: (~subset(X2, Y) | (~subset(Y, X2) | X2=Y))).
% 7.31/1.40
% 7.31/1.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.31/1.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.31/1.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.31/1.40 fresh(y, y, x1...xn) = u
% 7.31/1.40 C => fresh(s, t, x1...xn) = v
% 7.31/1.40 where fresh is a fresh function symbol and x1..xn are the free
% 7.31/1.40 variables of u and v.
% 7.31/1.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.31/1.40 input problem has no model of domain size 1).
% 7.31/1.40
% 7.31/1.40 The encoding turns the above axioms into the following unit equations and goals:
% 7.31/1.40
% 7.31/1.40 Axiom 1 (a_function): function(a_function) = true2.
% 7.31/1.40 Axiom 2 (member_of_domain): member(a, domain_of(a_function)) = true2.
% 7.31/1.40 Axiom 3 (two_sets_equal): fresh5(X, X, Y, Z) = Y.
% 7.31/1.40 Axiom 4 (two_sets_equal): fresh4(X, X, Y, Z) = Z.
% 7.31/1.40 Axiom 5 (apply_for_composition1): fresh142(X, X, Y, Z, W) = true2.
% 7.31/1.40 Axiom 6 (apply_for_composition2): fresh135(X, X, Y, Z, W) = true2.
% 7.31/1.40 Axiom 7 (two_sets_equal): fresh5(subset(X, Y), true2, Y, X) = fresh4(subset(Y, X), true2, Y, X).
% 7.31/1.40 Axiom 8 (apply_for_composition1): fresh141(function(X), true2, X, Y, Z) = subset(apply(Z, apply(X, Y)), apply(compose(Z, X), Y)).
% 7.31/1.40 Axiom 9 (apply_for_composition2): fresh135(function(X), true2, X, Y, Z) = subset(apply(compose(Y, X), Z), apply(Y, apply(X, Z))).
% 7.31/1.40 Axiom 10 (apply_for_composition1): fresh141(X, X, Y, Z, W) = fresh142(member(Z, domain_of(Y)), true2, Y, Z, W).
% 7.31/1.40
% 7.31/1.40 Goal 1 (prove_apply_for_composition3): apply(another_function, apply(a_function, a)) = apply(compose(another_function, a_function), a).
% 7.31/1.40 Proof:
% 7.31/1.40 apply(another_function, apply(a_function, a))
% 7.31/1.40 = { by axiom 3 (two_sets_equal) R->L }
% 7.31/1.40 fresh5(true2, true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 6 (apply_for_composition2) R->L }
% 7.31/1.40 fresh5(fresh135(true2, true2, a_function, another_function, a), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 1 (a_function) R->L }
% 7.31/1.40 fresh5(fresh135(function(a_function), true2, a_function, another_function, a), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 9 (apply_for_composition2) }
% 7.31/1.40 fresh5(subset(apply(compose(another_function, a_function), a), apply(another_function, apply(a_function, a))), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 7 (two_sets_equal) }
% 7.31/1.40 fresh4(subset(apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a)), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 8 (apply_for_composition1) R->L }
% 7.31/1.40 fresh4(fresh141(function(a_function), true2, a_function, a, another_function), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 1 (a_function) }
% 7.31/1.40 fresh4(fresh141(true2, true2, a_function, a, another_function), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 10 (apply_for_composition1) }
% 7.31/1.40 fresh4(fresh142(member(a, domain_of(a_function)), true2, a_function, a, another_function), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 2 (member_of_domain) }
% 7.31/1.40 fresh4(fresh142(true2, true2, a_function, a, another_function), true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 5 (apply_for_composition1) }
% 7.31/1.40 fresh4(true2, true2, apply(another_function, apply(a_function, a)), apply(compose(another_function, a_function), a))
% 7.31/1.40 = { by axiom 4 (two_sets_equal) }
% 7.31/1.40 apply(compose(another_function, a_function), a)
% 7.31/1.40 % SZS output end Proof
% 7.31/1.40
% 7.31/1.40 RESULT: Unsatisfiable (the axioms are contradictory).
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