TSTP Solution File: GRP452-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP452-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n004.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 01:15:02 EDT 2023
% Result : Unsatisfiable 0.83s 1.19s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP452-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Aug 28 22:37:07 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.83/1.19 % SZS status Unsatisfiable
% 0.83/1.19 % SZS output start Proof
% 0.83/1.19 original problem:
% 0.83/1.19 axioms:
% 0.83/1.19 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) = B
% 0.83/1.19 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.83/1.19 inverse(A) = divide(divide(B, B), A)
% 0.83/1.19 goal:
% 0.83/1.19 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.83/1.19 To show the unsatisfiability of the original goal,
% 0.83/1.19 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.83/1.19 Here is an equational proof:
% 0.83/1.19 0: divide(divide(divide(X0, X0), divide(X0, divide(X1, divide(divide(divide(X0, X0), X0), X2)))), X2) = X1.
% 0.83/1.19 Proof: Axiom.
% 0.83/1.19
% 0.83/1.19 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.83/1.19 Proof: Axiom.
% 0.83/1.19
% 0.83/1.19 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.83/1.19 Proof: Axiom.
% 0.83/1.19
% 0.83/1.19 3: divide(inverse(divide(X0, divide(X1, divide(inverse(X0), X2)))), X2) = X1.
% 0.83/1.19 Proof: Rewrite equation 0,
% 0.83/1.19 lhs with equations [2,2]
% 0.83/1.19 rhs with equations [].
% 0.83/1.19
% 0.83/1.19 4: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.83/1.19 Proof: Rewrite equation 1,
% 0.83/1.19 lhs with equations []
% 0.83/1.19 rhs with equations [2].
% 0.83/1.19
% 0.83/1.19 10: divide(X3, X3) = divide(inverse(divide(X0, inverse(divide(inverse(X0), X2)))), X2).
% 0.83/1.19 Proof: A critical pair between equations 3 and 2.
% 0.83/1.19
% 0.83/1.19 12: X1 = divide(inverse(divide(divide(X3, divide(X4, divide(inverse(X3), X5))), divide(X1, X4))), X5).
% 0.83/1.19 Proof: A critical pair between equations 3 and 3.
% 0.83/1.19
% 0.83/1.19 13: inverse(divide(X3, divide(X4, divide(inverse(X3), divide(inverse(X0), X2))))) = divide(inverse(divide(X0, X4)), X2).
% 0.83/1.19 Proof: A critical pair between equations 3 and 3.
% 0.83/1.19
% 0.83/1.19 14: X1 = inverse(divide(X3, divide(divide(X1, X4), divide(inverse(X3), X4)))).
% 0.83/1.19 Proof: Rewrite equation 12,
% 0.83/1.19 lhs with equations []
% 0.83/1.19 rhs with equations [13,3].
% 0.83/1.19
% 0.83/1.19 16: X5 = inverse(divide(X3, inverse(divide(inverse(X3), X5)))).
% 0.83/1.19 Proof: A critical pair between equations 14 and 2.
% 0.83/1.19
% 0.83/1.19 23: X6 = divide(divide(inverse(divide(X7, X6)), X8), divide(inverse(X7), X8)).
% 0.83/1.19 Proof: A critical pair between equations 3 and 13.
% 0.83/1.19
% 0.83/1.19 33: divide(X3, X3) = divide(X2, X2).
% 0.83/1.19 Proof: Rewrite equation 10,
% 0.83/1.19 lhs with equations []
% 0.83/1.19 rhs with equations [16].
% 0.83/1.19
% 0.83/1.19 38: inverse(divide(X1, X1)) = divide(X5, X5).
% 0.83/1.19 Proof: A critical pair between equations 2 and 33.
% 0.83/1.19
% 0.83/1.19 42: inverse(X3) = inverse(divide(X3, divide(X6, X6))).
% 0.83/1.19 Proof: A critical pair between equations 14 and 33.
% 0.83/1.19
% 0.83/1.19 44: X6 = inverse(divide(inverse(X7), inverse(divide(X7, X6)))).
% 0.83/1.19 Proof: A critical pair between equations 23 and 2.
% 0.83/1.19
% 0.83/1.19 59: X8 = inverse(divide(inverse(X8), divide(X9, X9))).
% 0.83/1.19 Proof: A critical pair between equations 44 and 38.
% 0.83/1.19
% 0.83/1.19 65: X8 = inverse(inverse(X8)).
% 0.83/1.19 Proof: Rewrite equation 59,
% 0.83/1.19 lhs with equations []
% 0.83/1.19 rhs with equations [42].
% 0.83/1.19
% 0.83/1.19 73: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.83/1.19 Proof: Rewrite lhs with equations [4,4,2,65]
% 0.83/1.19 rhs with equations [].
% 0.83/1.19
% 0.83/1.19 % SZS output end Proof
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