TSTP Solution File: KRS093+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS093+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n025.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 05:52:52 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS093+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 02:31:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 Take the following subset of the input axioms:
% 0.21/0.39 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.21/0.39 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.21/0.39 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (cf(X2) & ce3(X2)))).
% 0.21/0.39 fof(axiom_3, axiom, ![X2]: (cc(X2) => ~cd(X2))).
% 0.21/0.39 fof(axiom_4, axiom, ![X2]: (cc1(X2) => ~cd1(X2))).
% 0.21/0.39 fof(axiom_6, axiom, ![X2]: (ce3(X2) => cc(X2))).
% 0.21/0.39 fof(axiom_7, axiom, ![X2]: (cf(X2) => cd(X2))).
% 0.21/0.39 fof(axiom_8, axiom, cUnsatisfiable(i2003_11_14_17_20_07201)).
% 0.21/0.39
% 0.21/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.39 fresh(y, y, x1...xn) = u
% 0.21/0.39 C => fresh(s, t, x1...xn) = v
% 0.21/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.39 variables of u and v.
% 0.21/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.39 input problem has no model of domain size 1).
% 0.21/0.39
% 0.21/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.39
% 0.21/0.39 Axiom 1 (axiom_8): cUnsatisfiable(i2003_11_14_17_20_07201) = true2.
% 0.21/0.39 Axiom 2 (axiom_7): fresh(X, X, Y) = true2.
% 0.21/0.39 Axiom 3 (axiom_2_1): fresh7(X, X, Y) = true2.
% 0.21/0.39 Axiom 4 (axiom_2): fresh6(X, X, Y) = true2.
% 0.21/0.39 Axiom 5 (axiom_6): fresh2(X, X, Y) = true2.
% 0.21/0.39 Axiom 6 (axiom_7): fresh(cf(X), true2, X) = cd(X).
% 0.21/0.39 Axiom 7 (axiom_2_1): fresh7(cUnsatisfiable(X), true2, X) = ce3(X).
% 0.21/0.39 Axiom 8 (axiom_2): fresh6(cUnsatisfiable(X), true2, X) = cf(X).
% 0.21/0.39 Axiom 9 (axiom_6): fresh2(ce3(X), true2, X) = cc(X).
% 0.21/0.39
% 0.21/0.39 Goal 1 (axiom_3): tuple(cc(X), cd(X)) = tuple(true2, true2).
% 0.21/0.39 The goal is true when:
% 0.21/0.39 X = i2003_11_14_17_20_07201
% 0.21/0.39
% 0.21/0.39 Proof:
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), cd(i2003_11_14_17_20_07201))
% 0.21/0.39 = { by axiom 6 (axiom_7) R->L }
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), fresh(cf(i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201))
% 0.21/0.39 = { by axiom 8 (axiom_2) R->L }
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), fresh(fresh6(cUnsatisfiable(i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201))
% 0.21/0.39 = { by axiom 1 (axiom_8) }
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), fresh(fresh6(true2, true2, i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201))
% 0.21/0.39 = { by axiom 4 (axiom_2) }
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), fresh(true2, true2, i2003_11_14_17_20_07201))
% 0.21/0.39 = { by axiom 2 (axiom_7) }
% 0.21/0.39 tuple(cc(i2003_11_14_17_20_07201), true2)
% 0.21/0.39 = { by axiom 9 (axiom_6) R->L }
% 0.21/0.39 tuple(fresh2(ce3(i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201), true2)
% 0.21/0.39 = { by axiom 7 (axiom_2_1) R->L }
% 0.21/0.39 tuple(fresh2(fresh7(cUnsatisfiable(i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201), true2)
% 0.21/0.39 = { by axiom 1 (axiom_8) }
% 0.21/0.39 tuple(fresh2(fresh7(true2, true2, i2003_11_14_17_20_07201), true2, i2003_11_14_17_20_07201), true2)
% 0.21/0.39 = { by axiom 3 (axiom_2_1) }
% 0.21/0.39 tuple(fresh2(true2, true2, i2003_11_14_17_20_07201), true2)
% 0.21/0.39 = { by axiom 5 (axiom_6) }
% 0.21/0.39 tuple(true2, true2)
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39
% 0.21/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------