TSTP Solution File: LCL190-3 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : LCL190-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n011.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 : 600s
% DateTime : Sun Jul 17 12:58:56 EDT 2022
% Result : Unsatisfiable 10.40s 10.19s
% Output : Proof 10.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL190-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 18:32:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.40/10.19 % SZS status Unsatisfiable
% 10.40/10.19 % SZS output start Proof
% 10.40/10.19 The input problem is unsatisfiable because
% 10.40/10.19
% 10.40/10.19 [1] the following set of Horn clauses is unsatisfiable:
% 10.40/10.19
% 10.40/10.19 axiom(implies(or(A, A), A))
% 10.40/10.19 axiom(implies(A, or(B, A)))
% 10.40/10.19 axiom(implies(or(A, B), or(B, A)))
% 10.40/10.19 axiom(implies(or(A, or(B, C)), or(B, or(A, C))))
% 10.40/10.19 axiom(implies(implies(A, B), implies(or(C, A), or(C, B))))
% 10.40/10.19 implies(X, Y) = or(not(X), Y)
% 10.40/10.19 axiom(X) ==> theorem(X)
% 10.40/10.19 theorem(implies(Y, X)) & theorem(Y) ==> theorem(X)
% 10.40/10.19 theorem(implies(or(p, or(q, r)), or(p, or(r, q)))) ==> \bottom
% 10.40/10.19
% 10.40/10.19 This holds because
% 10.40/10.19
% 10.40/10.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 10.40/10.19
% 10.40/10.19 E:
% 10.40/10.19 axiom(implies(A, or(B, A))) = true__
% 10.40/10.19 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true__
% 10.40/10.19 axiom(implies(or(A, A), A)) = true__
% 10.40/10.19 axiom(implies(or(A, B), or(B, A))) = true__
% 10.40/10.19 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true__
% 10.40/10.19 f1(axiom(X), X) = true__
% 10.40/10.19 f1(true__, X) = theorem(X)
% 10.40/10.19 f2(true__, X) = theorem(X)
% 10.40/10.19 f3(theorem(Y), Y, X) = true__
% 10.40/10.19 f3(true__, Y, X) = f2(theorem(implies(Y, X)), X)
% 10.40/10.19 f4(theorem(implies(or(p, or(q, r)), or(p, or(r, q))))) = true__
% 10.40/10.19 f4(true__) = false__
% 10.40/10.19 implies(X, Y) = or(not(X), Y)
% 10.40/10.19 G:
% 10.40/10.19 true__ = false__
% 10.40/10.19
% 10.40/10.19 This holds because
% 10.40/10.19
% 10.40/10.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 10.40/10.19
% 10.40/10.19
% 10.40/10.19 axiom(implies(A, or(B, A))) -> true__
% 10.40/10.19 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) -> true__
% 10.40/10.19 axiom(implies(or(A, A), A)) -> true__
% 10.40/10.19 axiom(implies(or(A, B), or(B, A))) -> true__
% 10.40/10.19 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) -> true__
% 10.40/10.19 axiom(or(not(Y0), or(Y1, Y0))) -> true__
% 10.40/10.19 axiom(or(not(or(Y0, Y0)), Y0)) -> true__
% 10.40/10.19 axiom(or(not(or(Y0, Y1)), or(Y1, Y0))) -> true__
% 10.40/10.19 axiom(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__
% 10.40/10.19 axiom(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))) -> true__
% 10.40/10.19 f1(axiom(X), X) -> true__
% 10.40/10.19 f1(true__, not(or(not(or(not(Y0), or(Y1, Y0))), not(or(not(Y0), or(Y1, Y0)))))) -> true__
% 10.40/10.19 f1(true__, not(or(not(or(not(or(Y0, Y0)), Y0)), not(or(not(or(Y0, Y0)), Y0))))) -> true__
% 10.40/10.19 f1(true__, not(or(not(or(not(or(Y0, Y1)), or(Y1, Y0))), not(or(not(or(Y0, Y1)), or(Y1, Y0)))))) -> true__
% 10.40/10.19 f1(true__, not(or(not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))), not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2))))))) -> true__
% 10.40/10.19 f1(true__, not(or(not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))), not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1))))))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(Y0), or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(or(Y0, Y0)), Y0))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(or(Y0, Y1)), or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2))))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 10.40/10.19 f1(true__, or(X1, or(not(or(or(X1, X2), or(X1, X2))), X2))) -> true__
% 10.40/10.19 f1(true__, or(Y0, not(or(Y0, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(Y1, or(not(Y0), Y0))) -> true__
% 10.40/10.19 f1(true__, or(Y1, or(not(or(Y0, Y1)), Y0))) -> true__
% 10.40/10.19 f1(true__, or(Y1, or(not(or(Y0, or(Y1, Y2))), or(Y0, Y2)))) -> true__
% 10.40/10.19 f1(true__, or(not(X0), or(X1, X0))) -> true__
% 10.40/10.19 f1(true__, or(not(X1), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(Y0), or(X2, or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(Y0), or(Y0, Y1))) -> true__
% 10.40/10.19 f1(true__, or(not(Y0), or(not(or(X3, X1)), or(X3, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X0, X0)), X0)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, not(or(not(Y0), or(Y1, Y0))))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, not(or(not(or(Y0, Y0)), Y0)))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, not(or(not(or(Y0, Y1)), or(Y1, Y0))))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, or(not(or(not(Y0), or(Y1, Y0))), X2))), or(X1, X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, or(not(or(not(or(Y0, Y0)), Y0)), X2))), or(X1, X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, or(not(or(not(or(Y0, Y1)), or(Y1, Y0))), X2))), or(X1, X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, or(not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))), X2))), or(X1, X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X1, or(not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))), X2))), or(X1, X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X2, Y0)), or(X2, or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X2, or(Y0, Y0))), or(X2, Y0))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X2, or(Y0, Y1))), or(X2, or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X2, or(Y0, or(Y1, Y2)))), or(X2, or(Y1, or(Y0, Y2))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(X2, or(not(Y0), Y1))), or(X2, or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, Y0)), or(X2, Y0))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, Y1)), or(X2, or(Y1, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, Y1)), or(Y0, Y1))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, not(X1))), or(not(or(X3, X1)), or(X3, Y0)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(X2, or(Y1, or(Y0, Y2))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(Y0, or(Y1, Y2)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, or(Y1, Y2))), or(or(Y0, Y2), Y1))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, or(not(X1), Y2))), or(not(or(X3, X1)), or(X3, or(Y0, Y2))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y0, or(or(Y0, Y2), Y2))), or(Y0, Y2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(Y2, Y0)), or(not(or(not(Y0), Y1)), or(Y2, Y1)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(Y0), X2)), or(not(or(Y0, Y0)), X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(Y0), Y1)), or(X2, or(not(or(Y2, Y0)), or(Y2, Y1))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(Y0), Y1)), or(Y2, or(not(or(Y2, Y0)), Y1)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(Y0), Y1)), or(not(or(X3, or(Y2, Y0))), or(X3, or(Y2, Y1))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(Y0), Y1)), or(or(Y2, Y1), not(or(Y2, Y0))))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(or(Y1, Y0)), X2)), or(not(Y0), X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(or(Y1, Y0)), X2)), or(not(or(Y0, Y1)), X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(or(Y1, or(Y0, Y2))), X2)), or(not(or(Y0, or(Y1, Y2))), X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(not(or(not(or(Y2, Y0)), or(Y2, Y1))), X2)), or(not(or(not(Y0), Y1)), X2))) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(X1, X1), or(X1, X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(X1, X2), or(X1, X2))), or(X2, X1))) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(X1, or(X2, X3)), or(X1, or(X2, X3)))), or(X2, or(X1, X3)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(X2, X3), Y1)), or(X2, or(Y1, X3)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(X1), X2), or(not(X1), X2))), or(not(or(X3, X1)), or(X3, X2)))) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(or(not(Y0), or(Y1, Y0))), X1), or(not(or(not(Y0), or(Y1, Y0))), X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(or(not(or(Y0, Y0)), Y0)), X1), or(not(or(not(or(Y0, Y0)), Y0)), X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(or(not(or(Y0, Y1)), or(Y1, Y0))), X1), or(not(or(not(or(Y0, Y1)), or(Y1, Y0))), X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))), X1), or(not(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))), X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(not(or(or(not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))), X1), or(not(or(not(or(not(Y0), Y1)), or(not(or(Y2, Y0)), or(Y2, Y1)))), X1))), X1)) -> true__
% 10.40/10.19 f1(true__, or(or(Y1, Y0), not(Y0))) -> true__
% 10.40/10.19 f1(true__, or(or(Y1, Y0), not(or(Y0, Y1)))) -> true__
% 10.40/10.19 f1(true__, or(or(Y1, or(Y0, Y2)), not(or(Y0, or(Y1, Y2))))) -> true__
% 10.40/10.19 f1(true__, or(or(not(or(Y2, Y0)), or(Y2, Y1)), not(or(not(Y0), Y1)))) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, not(or(X0, X0)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(X1), X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(X1), or(X2, X1)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(X1, X0)), X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(X1, X1)), X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(X1, X2)), or(X2, X1)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(X1, or(X0, X2))), or(X1, X2)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(X1, or(X2, X3))), or(X2, or(X1, X3))))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(not(X1), X2)), or(not(or(X3, X1)), or(X3, X2))))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(X0, or(not(or(or(X0, X1), or(X0, X1))), X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(X0), or(X1, X0))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, X0)), X0)), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, X1)), or(X0, or(X2, X1)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, X1)), or(X1, X0))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, X1)), or(not(or(not(X1), X2)), or(X0, X2)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, or(X1, X1))), or(X0, X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, or(X1, X2))), or(X0, or(X2, X1)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, or(X1, or(X2, X3)))), or(X0, or(X2, or(X1, X3))))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(X0, or(not(X1), X2))), or(X0, or(not(or(X3, X1)), or(X3, X2))))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(or(X0, X1), not(X1))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(or(X0, X1), not(or(X1, X0)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(or(X0, or(X1, X2)), not(or(X1, or(X0, X2))))), Y1)), Y1) -> true__
% 10.40/10.19 f2(f1(true__, or(not(or(or(not(or(X0, X1)), or(X0, X2)), not(or(not(X1), X2)))), Y1)), Y1) -> true__
% 10.40/10.19 f2(true__, X) -> theorem(X)
% 10.40/10.19 f3(f1(true__, Y0), Y0, Y1) -> true__
% 10.40/10.19 f3(theorem(Y), Y, X) -> true__
% 10.40/10.19 f3(true__, Y, X) -> f2(theorem(implies(Y, X)), X)
% 10.40/10.19 f4(f1(true__, or(not(or(p, or(q, r))), or(p, or(r, q))))) -> true__
% 10.40/10.19 f4(theorem(implies(or(p, or(q, r)), or(p, or(r, q))))) -> true__
% 10.40/10.19 f4(true__) -> false__
% 10.40/10.19 false__ -> true__
% 10.40/10.19 implies(X, Y) -> or(not(X), Y)
% 10.40/10.19 theorem(X) -> f1(true__, X)
% 10.40/10.19 with the LPO induced by
% 10.40/10.19 r > q > p > f4 > f3 > f2 > theorem > f1 > axiom > implies > not > or > false__ > true__
% 10.40/10.19
% 10.40/10.19 % SZS output end Proof
% 10.40/10.19
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