TSTP Solution File: PUZ131+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ131+1 : TPTP v8.1.2. Released v4.1.0.
% 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 13:24:22 EDT 2023
% Result : Theorem 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ131+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 22:58:23 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.23/0.44
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44
% 0.23/0.44 % SZS output start Proof
% 0.23/0.45 Take the following subset of the input axioms:
% 0.23/0.45 fof(coordinator_teaches, axiom, ![X]: (course(X) => teaches(coordinatorof(X), X))).
% 0.23/0.45 fof(csc410_type, axiom, course(csc410)).
% 0.23/0.45 fof(michael_enrolled_csc410_axiom, axiom, enrolled(michael, csc410)).
% 0.23/0.45 fof(michael_type, axiom, student(michael)).
% 0.23/0.45 fof(student_enrolled_taught, axiom, ![Y, X2]: ((student(X2) & course(Y)) => (enrolled(X2, Y) => ![Z]: (professor(Z) => (teaches(Z, Y) => taughtby(X2, Z)))))).
% 0.23/0.45 fof(teaching_conjecture, conjecture, taughtby(michael, victor)).
% 0.23/0.45 fof(victor_coordinator_csc410_axiom, axiom, coordinatorof(csc410)=victor).
% 0.23/0.45 fof(victor_type, axiom, professor(victor)).
% 0.23/0.45
% 0.23/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.45 fresh(y, y, x1...xn) = u
% 0.23/0.45 C => fresh(s, t, x1...xn) = v
% 0.23/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.45 variables of u and v.
% 0.23/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.45 input problem has no model of domain size 1).
% 0.23/0.45
% 0.23/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.45
% 0.23/0.45 Axiom 1 (victor_coordinator_csc410_axiom): coordinatorof(csc410) = victor.
% 0.23/0.45 Axiom 2 (michael_type): student(michael) = true.
% 0.23/0.45 Axiom 3 (victor_type): professor(victor) = true.
% 0.23/0.45 Axiom 4 (csc410_type): course(csc410) = true.
% 0.23/0.45 Axiom 5 (michael_enrolled_csc410_axiom): enrolled(michael, csc410) = true.
% 0.23/0.45 Axiom 6 (coordinator_teaches): fresh10(X, X, Y) = true.
% 0.23/0.45 Axiom 7 (student_enrolled_taught): fresh15(X, X, Y, Z) = true.
% 0.23/0.45 Axiom 8 (student_enrolled_taught): fresh13(X, X, Y, Z) = taughtby(Y, Z).
% 0.23/0.45 Axiom 9 (coordinator_teaches): fresh10(course(X), true, X) = teaches(coordinatorof(X), X).
% 0.23/0.45 Axiom 10 (student_enrolled_taught): fresh14(X, X, Y, Z) = fresh15(student(Y), true, Y, Z).
% 0.23/0.45 Axiom 11 (student_enrolled_taught): fresh12(X, X, Y, Z, W) = fresh13(professor(W), true, Y, W).
% 0.23/0.45 Axiom 12 (student_enrolled_taught): fresh11(X, X, Y, Z, W) = fresh14(course(Z), true, Y, W).
% 0.23/0.45 Axiom 13 (student_enrolled_taught): fresh11(teaches(X, Y), true, Z, Y, X) = fresh12(enrolled(Z, Y), true, Z, Y, X).
% 0.23/0.45
% 0.23/0.45 Goal 1 (teaching_conjecture): taughtby(michael, victor) = true.
% 0.23/0.45 Proof:
% 0.23/0.45 taughtby(michael, victor)
% 0.23/0.45 = { by axiom 8 (student_enrolled_taught) R->L }
% 0.23/0.45 fresh13(true, true, michael, victor)
% 0.23/0.45 = { by axiom 3 (victor_type) R->L }
% 0.23/0.45 fresh13(professor(victor), true, michael, victor)
% 0.23/0.45 = { by axiom 11 (student_enrolled_taught) R->L }
% 0.23/0.45 fresh12(true, true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 5 (michael_enrolled_csc410_axiom) R->L }
% 0.23/0.45 fresh12(enrolled(michael, csc410), true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 13 (student_enrolled_taught) R->L }
% 0.23/0.45 fresh11(teaches(victor, csc410), true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 1 (victor_coordinator_csc410_axiom) R->L }
% 0.23/0.45 fresh11(teaches(coordinatorof(csc410), csc410), true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 9 (coordinator_teaches) R->L }
% 0.23/0.45 fresh11(fresh10(course(csc410), true, csc410), true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 4 (csc410_type) }
% 0.23/0.45 fresh11(fresh10(true, true, csc410), true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 6 (coordinator_teaches) }
% 0.23/0.45 fresh11(true, true, michael, csc410, victor)
% 0.23/0.45 = { by axiom 12 (student_enrolled_taught) }
% 0.23/0.45 fresh14(course(csc410), true, michael, victor)
% 0.23/0.45 = { by axiom 4 (csc410_type) }
% 0.23/0.45 fresh14(true, true, michael, victor)
% 0.23/0.45 = { by axiom 10 (student_enrolled_taught) }
% 0.23/0.45 fresh15(student(michael), true, michael, victor)
% 0.23/0.45 = { by axiom 2 (michael_type) }
% 0.23/0.45 fresh15(true, true, michael, victor)
% 0.23/0.45 = { by axiom 7 (student_enrolled_taught) }
% 0.23/0.45 true
% 0.23/0.45 % SZS output end Proof
% 0.23/0.45
% 0.23/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------