TSTP Solution File: ROB002-1 by Toma---0.4
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% File : Toma---0.4
% Problem : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% 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 14:08:59 EDT 2023
% Result : Unsatisfiable 0.94s 1.26s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ROB002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.12/0.35 % Computer : n001.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 07:32:34 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.94/1.26 % SZS status Unsatisfiable
% 0.94/1.26 % SZS output start Proof
% 0.94/1.26 original problem:
% 0.94/1.26 axioms:
% 0.94/1.26 add(X, Y) = add(Y, X)
% 0.94/1.26 add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.94/1.26 negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 0.94/1.26 negate(negate(X)) = X
% 0.94/1.26 goal:
% 0.94/1.26 add(negate(add(a(), negate(b()))), negate(add(negate(a()), negate(b())))) != b()
% 0.94/1.26 To show the unsatisfiability of the original goal,
% 0.94/1.26 it suffices to show that add(negate(add(a(), negate(b()))), negate(add(negate(a()), negate(b())))) = b() (skolemized goal) is valid under the axioms.
% 0.94/1.26 Here is an equational proof:
% 0.94/1.26 0: add(X0, X1) = add(X1, X0).
% 0.94/1.26 Proof: Axiom.
% 0.94/1.26
% 0.94/1.26 1: add(add(X0, X1), X2) = add(X0, add(X1, X2)).
% 0.94/1.26 Proof: Axiom.
% 0.94/1.26
% 0.94/1.26 2: negate(add(negate(add(X0, X1)), negate(add(X0, negate(X1))))) = X0.
% 0.94/1.26 Proof: Axiom.
% 0.94/1.26
% 0.94/1.26 3: negate(negate(X0)) = X0.
% 0.94/1.26 Proof: Axiom.
% 0.94/1.26
% 0.94/1.26 5: add(X3, add(X4, X2)) = add(add(X4, X3), X2).
% 0.94/1.26 Proof: A critical pair between equations 1 and 0.
% 0.94/1.26
% 0.94/1.26 8: add(negate(add(X2, X3)), negate(add(X2, negate(X3)))) = negate(X2).
% 0.94/1.26 Proof: A critical pair between equations 3 and 2.
% 0.94/1.26
% 0.94/1.26 10: add(X3, X4) = negate(add(negate(add(add(X3, X4), X1)), negate(add(X3, add(X4, negate(X1)))))).
% 0.94/1.26 Proof: A critical pair between equations 2 and 1.
% 0.94/1.26
% 0.94/1.26 11: add(X3, X4) = negate(add(negate(add(X3, add(X4, X5))), negate(add(add(X3, X4), negate(X5))))).
% 0.94/1.26 Proof: A critical pair between equations 2 and 1.
% 0.94/1.26
% 0.94/1.26 15: add(X3, X4) = negate(add(negate(add(X3, add(X4, X5))), negate(add(X4, add(X3, negate(X5)))))).
% 0.94/1.26 Proof: Rewrite equation 11,
% 0.94/1.26 lhs with equations []
% 0.94/1.26 rhs with equations [5].
% 0.94/1.26
% 0.94/1.26 16: add(X3, X4) = add(X4, X3).
% 0.94/1.26 Proof: Rewrite equation 10,
% 0.94/1.26 lhs with equations []
% 0.94/1.26 rhs with equations [5,15].
% 0.94/1.26
% 0.94/1.26 24: negate(X5) = add(negate(add(X6, X5)), negate(add(X5, negate(X6)))).
% 0.94/1.26 Proof: A critical pair between equations 8 and 16.
% 0.94/1.26
% 0.94/1.26 39: negate(X7) = add(negate(add(X6, X7)), negate(add(negate(X6), X7))).
% 0.94/1.26 Proof: A critical pair between equations 24 and 0.
% 0.94/1.26
% 0.94/1.26 49: add(negate(add(a(), negate(b()))), negate(add(negate(a()), negate(b())))) = b().
% 0.94/1.26 Proof: Rewrite lhs with equations [39,3]
% 0.94/1.26 rhs with equations [].
% 0.94/1.26
% 0.94/1.26 % SZS output end Proof
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