TSTP Solution File: GRP457-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP457-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 01:15:03 EDT 2023
% Result : Unsatisfiable 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP457-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:16:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 original problem:
% 0.19/0.42 axioms:
% 0.19/0.42 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity(), A), C)))), C) = B
% 0.19/0.42 multiply(A, B) = divide(A, divide(identity(), B))
% 0.19/0.42 inverse(A) = divide(identity(), A)
% 0.19/0.42 identity() = divide(A, A)
% 0.19/0.42 goal:
% 0.19/0.42 multiply(inverse(a1()), a1()) != identity()
% 0.19/0.42 To show the unsatisfiability of the original goal,
% 0.19/0.42 it suffices to show that multiply(inverse(a1()), a1()) = identity() (skolemized goal) is valid under the axioms.
% 0.19/0.42 Here is an equational proof:
% 0.19/0.42 1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.19/0.42 Proof: Axiom.
% 0.19/0.42
% 0.19/0.42 2: inverse(X0) = divide(identity(), X0).
% 0.19/0.42 Proof: Axiom.
% 0.19/0.42
% 0.19/0.42 3: identity() = divide(X0, X0).
% 0.19/0.42 Proof: Axiom.
% 0.19/0.42
% 0.19/0.42 5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.19/0.42 Proof: Rewrite equation 1,
% 0.19/0.42 lhs with equations []
% 0.19/0.42 rhs with equations [2].
% 0.19/0.42
% 0.19/0.42 6: multiply(inverse(a1()), a1()) = identity().
% 0.19/0.42 Proof: Rewrite lhs with equations [5,3]
% 0.19/0.42 rhs with equations [].
% 0.19/0.42
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------