TSTP Solution File: SET676+3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n015.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 15:32:57 EDT 2023
% Result : Theorem 0.21s 1.03s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.66 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.67 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.88 % Computer : n015.cluster.edu
% 0.19/0.88 % Model : x86_64 x86_64
% 0.19/0.88 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.88 % Memory : 8042.1875MB
% 0.19/0.88 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.88 % CPULimit : 300
% 0.19/0.88 % WCLimit : 300
% 0.19/0.88 % DateTime : Sat Aug 26 12:30:53 EDT 2023
% 0.19/0.88 % CPUTime :
% 0.21/1.03 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/1.03
% 0.21/1.03 % SZS status Theorem
% 0.21/1.03
% 0.21/1.04 % SZS output start Proof
% 0.21/1.04 Take the following subset of the input axioms:
% 0.21/1.04 fof(p1, axiom, ![B]: (ilf_type(B, set_type) => ![C]: (ilf_type(C, set_type) => ilf_type(cross_product(B, C), relation_type(B, C))))).
% 0.21/1.04 fof(p19, axiom, ![B2]: ilf_type(B2, set_type)).
% 0.21/1.04 fof(p4, axiom, ![B2]: (ilf_type(B2, set_type) => ![C2]: (ilf_type(C2, set_type) => (ilf_type(C2, identity_relation_of_type(B2)) <=> ilf_type(C2, relation_type(B2, B2)))))).
% 0.21/1.04 fof(prove_relset_1_41, conjecture, ![B2]: (ilf_type(B2, set_type) => ilf_type(cross_product(B2, B2), identity_relation_of_type(B2)))).
% 0.21/1.04
% 0.21/1.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/1.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/1.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/1.04 fresh(y, y, x1...xn) = u
% 0.21/1.04 C => fresh(s, t, x1...xn) = v
% 0.21/1.04 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/1.04 variables of u and v.
% 0.21/1.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/1.04 input problem has no model of domain size 1).
% 0.21/1.04
% 0.21/1.04 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/1.04
% 0.21/1.04 Axiom 1 (p19): ilf_type(X, set_type) = true2.
% 0.21/1.04 Axiom 2 (p4): fresh56(X, X, Y, Z) = true2.
% 0.21/1.04 Axiom 3 (p1): fresh21(X, X, Y, Z) = true2.
% 0.21/1.04 Axiom 4 (p4): fresh11(X, X, Y, Z) = ilf_type(Z, identity_relation_of_type(Y)).
% 0.21/1.04 Axiom 5 (p4): fresh55(X, X, Y, Z) = fresh56(ilf_type(Y, set_type), true2, Y, Z).
% 0.21/1.04 Axiom 6 (p1): fresh20(ilf_type(X, set_type), true2, Y, X) = fresh21(ilf_type(Y, set_type), true2, Y, X).
% 0.21/1.04 Axiom 7 (p1): fresh20(X, X, Y, Z) = ilf_type(cross_product(Y, Z), relation_type(Y, Z)).
% 0.21/1.04 Axiom 8 (p4): fresh55(ilf_type(X, relation_type(Y, Y)), true2, Y, X) = fresh11(ilf_type(X, set_type), true2, Y, X).
% 0.21/1.04
% 0.21/1.04 Goal 1 (prove_relset_1_41_1): ilf_type(cross_product(b, b), identity_relation_of_type(b)) = true2.
% 0.21/1.04 Proof:
% 0.21/1.04 ilf_type(cross_product(b, b), identity_relation_of_type(b))
% 0.21/1.04 = { by axiom 4 (p4) R->L }
% 0.21/1.04 fresh11(true2, true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 1 (p19) R->L }
% 0.21/1.04 fresh11(ilf_type(cross_product(b, b), set_type), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 8 (p4) R->L }
% 0.21/1.04 fresh55(ilf_type(cross_product(b, b), relation_type(b, b)), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 7 (p1) R->L }
% 0.21/1.04 fresh55(fresh20(true2, true2, b, b), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 1 (p19) R->L }
% 0.21/1.04 fresh55(fresh20(ilf_type(b, set_type), true2, b, b), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 6 (p1) }
% 0.21/1.04 fresh55(fresh21(ilf_type(b, set_type), true2, b, b), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 1 (p19) }
% 0.21/1.04 fresh55(fresh21(true2, true2, b, b), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 3 (p1) }
% 0.21/1.04 fresh55(true2, true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 5 (p4) }
% 0.21/1.04 fresh56(ilf_type(b, set_type), true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 1 (p19) }
% 0.21/1.04 fresh56(true2, true2, b, cross_product(b, b))
% 0.21/1.04 = { by axiom 2 (p4) }
% 0.21/1.04 true2
% 0.21/1.04 % SZS output end Proof
% 0.21/1.04
% 0.21/1.04 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------