TSTP Solution File: SEU308+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SEU308+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n023.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 17:52:08 EDT 2023
% Result : Theorem 177.79s 22.96s
% Output : Proof 177.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU308+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % 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 : n023.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 : Wed Aug 23 18:14:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 177.79/22.96 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 177.79/22.96
% 177.79/22.96 % SZS status Theorem
% 177.79/22.96
% 177.79/22.96 % SZS output start Proof
% 177.79/22.96 Take the following subset of the input axioms:
% 177.79/22.96 fof(d3_pre_topc, axiom, ![A2]: (one_sorted_str(A2) => cast_as_carrier_subset(A2)=the_carrier(A2))).
% 177.79/22.96 fof(d4_subset_1, axiom, ![A]: cast_to_subset(A)=A).
% 177.79/22.96 fof(d5_subset_1, axiom, ![B, A2_2]: (element(B, powerset(A2_2)) => subset_complement(A2_2, B)=set_difference(A2_2, B))).
% 177.79/22.96 fof(dt_k2_subset_1, axiom, ![A3]: element(cast_to_subset(A3), powerset(A3))).
% 177.79/22.96 fof(redefinition_k6_subset_1, axiom, ![C, B2, A2_2]: ((element(B2, powerset(A2_2)) & element(C, powerset(A2_2))) => subset_difference(A2_2, B2, C)=set_difference(B2, C))).
% 177.79/22.96 fof(t17_pre_topc, conjecture, ![A3]: (one_sorted_str(A3) => ![B2]: (element(B2, powerset(the_carrier(A3))) => subset_complement(the_carrier(A3), B2)=subset_difference(the_carrier(A3), cast_as_carrier_subset(A3), B2)))).
% 177.79/22.96
% 177.79/22.96 Now clausify the problem and encode Horn clauses using encoding 3 of
% 177.79/22.96 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 177.79/22.96 We repeatedly replace C & s=t => u=v by the two clauses:
% 177.79/22.96 fresh(y, y, x1...xn) = u
% 177.79/22.96 C => fresh(s, t, x1...xn) = v
% 177.79/22.96 where fresh is a fresh function symbol and x1..xn are the free
% 177.79/22.96 variables of u and v.
% 177.79/22.96 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 177.79/22.96 input problem has no model of domain size 1).
% 177.79/22.96
% 177.79/22.96 The encoding turns the above axioms into the following unit equations and goals:
% 177.79/22.96
% 177.79/22.96 Axiom 1 (t17_pre_topc_1): one_sorted_str(a) = true2.
% 177.79/22.96 Axiom 2 (d4_subset_1): cast_to_subset(X) = X.
% 177.79/22.96 Axiom 3 (d3_pre_topc): fresh738(X, X, Y) = the_carrier(Y).
% 177.79/22.96 Axiom 4 (t17_pre_topc): element(b6, powerset(the_carrier(a))) = true2.
% 177.79/22.96 Axiom 5 (dt_k2_subset_1): element(cast_to_subset(X), powerset(X)) = true2.
% 177.79/22.96 Axiom 6 (d3_pre_topc): fresh738(one_sorted_str(X), true2, X) = cast_as_carrier_subset(X).
% 177.79/22.96 Axiom 7 (d5_subset_1): fresh672(X, X, Y, Z) = set_difference(Y, Z).
% 177.79/22.96 Axiom 8 (redefinition_k6_subset_1): fresh444(X, X, Y, Z, W) = set_difference(Z, W).
% 177.79/22.96 Axiom 9 (redefinition_k6_subset_1): fresh443(X, X, Y, Z, W) = subset_difference(Y, Z, W).
% 177.79/22.96 Axiom 10 (d5_subset_1): fresh672(element(X, powerset(Y)), true2, Y, X) = subset_complement(Y, X).
% 177.79/22.96 Axiom 11 (redefinition_k6_subset_1): fresh443(element(X, powerset(Y)), true2, Y, Z, X) = fresh444(element(Z, powerset(Y)), true2, Y, Z, X).
% 177.79/22.96
% 177.79/22.96 Goal 1 (t17_pre_topc_2): subset_complement(the_carrier(a), b6) = subset_difference(the_carrier(a), cast_as_carrier_subset(a), b6).
% 177.79/22.96 Proof:
% 177.79/22.96 subset_complement(the_carrier(a), b6)
% 177.79/22.96 = { by axiom 10 (d5_subset_1) R->L }
% 177.79/22.96 fresh672(element(b6, powerset(the_carrier(a))), true2, the_carrier(a), b6)
% 177.79/22.96 = { by axiom 4 (t17_pre_topc) }
% 177.79/22.96 fresh672(true2, true2, the_carrier(a), b6)
% 177.79/22.96 = { by axiom 7 (d5_subset_1) }
% 177.79/22.96 set_difference(the_carrier(a), b6)
% 177.79/22.96 = { by axiom 8 (redefinition_k6_subset_1) R->L }
% 177.79/22.96 fresh444(true2, true2, the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 5 (dt_k2_subset_1) R->L }
% 177.79/22.96 fresh444(element(cast_to_subset(the_carrier(a)), powerset(the_carrier(a))), true2, the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 2 (d4_subset_1) }
% 177.79/22.96 fresh444(element(the_carrier(a), powerset(the_carrier(a))), true2, the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 11 (redefinition_k6_subset_1) R->L }
% 177.79/22.96 fresh443(element(b6, powerset(the_carrier(a))), true2, the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 4 (t17_pre_topc) }
% 177.79/22.96 fresh443(true2, true2, the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 9 (redefinition_k6_subset_1) }
% 177.79/22.96 subset_difference(the_carrier(a), the_carrier(a), b6)
% 177.79/22.96 = { by axiom 3 (d3_pre_topc) R->L }
% 177.79/22.96 subset_difference(the_carrier(a), fresh738(true2, true2, a), b6)
% 177.79/22.96 = { by axiom 1 (t17_pre_topc_1) R->L }
% 177.79/22.96 subset_difference(the_carrier(a), fresh738(one_sorted_str(a), true2, a), b6)
% 177.79/22.96 = { by axiom 6 (d3_pre_topc) }
% 177.79/22.96 subset_difference(the_carrier(a), cast_as_carrier_subset(a), b6)
% 177.79/22.96 % SZS output end Proof
% 177.79/22.96
% 177.79/22.96 RESULT: Theorem (the conjecture is true).
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