TSTP Solution File: KRS099+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KRS099+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 : n001.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 05:52:53 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS099+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 01:57:19 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --no-flatten-goal
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Take the following subset of the input axioms:
% 0.21/0.42 fof(axiom_0, axiom, ![X]: (cowlThing(X) & ~cowlNothing(X))).
% 0.21/0.42 fof(axiom_1, axiom, ![X2]: (xsd_string(X2) <=> ~xsd_integer(X2))).
% 0.21/0.42 fof(axiom_2, axiom, ![X2]: (cUnsatisfiable(X2) <=> (?[Y0, Y1, Y2]: (rtt(X2, Y0) & (rtt(X2, Y1) & (rtt(X2, Y2) & (Y0!=Y1 & (Y0!=Y2 & Y1!=Y2))))) & (![Y]: (rtt(X2, Y) => ca(Y)) & (![Y0_2, Y1_2]: ((rtt(X2, Y0_2) & rtt(X2, Y1_2)) => Y0_2=Y1_2) & ![Y0_2, Y1_2]: ((rtt(X2, Y0_2) & rtt(X2, Y1_2)) => Y0_2=Y1_2)))))).
% 0.21/0.42 fof(axiom_4, axiom, ![X2]: (cc(X2) => ~cd(X2))).
% 0.21/0.42 fof(axiom_5, axiom, cUnsatisfiable(i2003_11_14_17_20_29215)).
% 0.21/0.42
% 0.21/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.42 fresh(y, y, x1...xn) = u
% 0.21/0.42 C => fresh(s, t, x1...xn) = v
% 0.21/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.42 variables of u and v.
% 0.21/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.42 input problem has no model of domain size 1).
% 0.21/0.42
% 0.21/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.42
% 0.21/0.42 Axiom 1 (axiom_5): cUnsatisfiable(i2003_11_14_17_20_29215) = true2.
% 0.21/0.42 Axiom 2 (axiom_2_6): fresh7(X, X, Y) = true2.
% 0.21/0.42 Axiom 3 (axiom_2_7): fresh6(X, X, Y) = true2.
% 0.21/0.42 Axiom 4 (axiom_2_10): fresh11(X, X, Y, Z) = Z.
% 0.21/0.42 Axiom 5 (axiom_2_6): fresh7(cUnsatisfiable(X), true2, X) = rtt(X, y1_3(X)).
% 0.21/0.42 Axiom 6 (axiom_2_7): fresh6(cUnsatisfiable(X), true2, X) = rtt(X, y2(X)).
% 0.21/0.42 Axiom 7 (axiom_2_10): fresh(X, X, Y, Z, W) = Z.
% 0.21/0.42 Axiom 8 (axiom_2_10): fresh10(X, X, Y, Z, W) = fresh11(cUnsatisfiable(Y), true2, Z, W).
% 0.21/0.43 Axiom 9 (axiom_2_10): fresh10(rtt(X, Y), true2, X, Z, Y) = fresh(rtt(X, Z), true2, X, Z, Y).
% 0.21/0.43
% 0.21/0.43 Goal 1 (axiom_2): tuple2(y1_3(X), cUnsatisfiable(X)) = tuple2(y2(X), true2).
% 0.21/0.43 The goal is true when:
% 0.21/0.43 X = i2003_11_14_17_20_29215
% 0.21/0.43
% 0.21/0.43 Proof:
% 0.21/0.43 tuple2(y1_3(i2003_11_14_17_20_29215), cUnsatisfiable(i2003_11_14_17_20_29215))
% 0.21/0.43 = { by axiom 1 (axiom_5) }
% 0.21/0.43 tuple2(y1_3(i2003_11_14_17_20_29215), true2)
% 0.21/0.43 = { by axiom 4 (axiom_2_10) R->L }
% 0.21/0.43 tuple2(fresh11(true2, true2, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 1 (axiom_5) R->L }
% 0.21/0.43 tuple2(fresh11(cUnsatisfiable(i2003_11_14_17_20_29215), true2, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 8 (axiom_2_10) R->L }
% 0.21/0.43 tuple2(fresh10(true2, true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 2 (axiom_2_6) R->L }
% 0.21/0.43 tuple2(fresh10(fresh7(true2, true2, i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 1 (axiom_5) R->L }
% 0.21/0.43 tuple2(fresh10(fresh7(cUnsatisfiable(i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 5 (axiom_2_6) }
% 0.21/0.43 tuple2(fresh10(rtt(i2003_11_14_17_20_29215, y1_3(i2003_11_14_17_20_29215)), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 9 (axiom_2_10) }
% 0.21/0.43 tuple2(fresh(rtt(i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215)), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 6 (axiom_2_7) R->L }
% 0.21/0.43 tuple2(fresh(fresh6(cUnsatisfiable(i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 1 (axiom_5) }
% 0.21/0.43 tuple2(fresh(fresh6(true2, true2, i2003_11_14_17_20_29215), true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 3 (axiom_2_7) }
% 0.21/0.43 tuple2(fresh(true2, true2, i2003_11_14_17_20_29215, y2(i2003_11_14_17_20_29215), y1_3(i2003_11_14_17_20_29215)), true2)
% 0.21/0.43 = { by axiom 7 (axiom_2_10) }
% 0.21/0.43 tuple2(y2(i2003_11_14_17_20_29215), true2)
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------