TSTP Solution File: BOO013-2 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n014.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 : Wed Aug 30 18:10:58 EDT 2023
% Result : Unsatisfiable 2.32s 2.68s
% Output : CNFRefutation 2.32s
% 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 : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n014.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 : Sun Aug 27 07:38:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.32/2.68 % SZS status Unsatisfiable
% 2.32/2.68 % SZS output start Proof
% 2.32/2.68 original problem:
% 2.32/2.68 axioms:
% 2.32/2.68 add(X, Y) = add(Y, X)
% 2.32/2.68 multiply(X, Y) = multiply(Y, X)
% 2.32/2.68 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 2.32/2.68 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 2.32/2.68 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 2.32/2.68 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 2.32/2.68 add(X, inverse(X)) = multiplicative_identity()
% 2.32/2.68 add(inverse(X), X) = multiplicative_identity()
% 2.32/2.68 multiply(X, inverse(X)) = additive_identity()
% 2.32/2.68 multiply(inverse(X), X) = additive_identity()
% 2.32/2.68 multiply(X, multiplicative_identity()) = X
% 2.32/2.68 multiply(multiplicative_identity(), X) = X
% 2.32/2.68 add(X, additive_identity()) = X
% 2.32/2.68 add(additive_identity(), X) = X
% 2.32/2.68 add(a(), b()) = multiplicative_identity()
% 2.32/2.68 add(a(), c()) = multiplicative_identity()
% 2.32/2.68 multiply(a(), b()) = additive_identity()
% 2.32/2.68 multiply(a(), c()) = additive_identity()
% 2.32/2.68 goal:
% 2.32/2.68 b() != c()
% 2.32/2.68 To show the unsatisfiability of the original goal,
% 2.32/2.68 it suffices to show that b() = c() (skolemized goal) is valid under the axioms.
% 2.32/2.68 Here is an equational proof:
% 2.32/2.68 0: add(X0, X1) = add(X1, X0).
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 1: multiply(X0, X1) = multiply(X1, X0).
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 4: multiply(add(X0, X1), X2) = add(multiply(X0, X2), multiply(X1, X2)).
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 5: multiply(X0, add(X1, X2)) = add(multiply(X0, X1), multiply(X0, X2)).
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 6: add(X0, inverse(X0)) = multiplicative_identity().
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 11: multiply(multiplicative_identity(), X0) = X0.
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 13: add(additive_identity(), X0) = X0.
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 14: add(a(), b()) = multiplicative_identity().
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 15: add(a(), c()) = multiplicative_identity().
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 16: multiply(a(), b()) = additive_identity().
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 17: multiply(a(), c()) = additive_identity().
% 2.32/2.68 Proof: Axiom.
% 2.32/2.68
% 2.32/2.68 22: add(multiply(a(), b()), X0) = X0.
% 2.32/2.68 Proof: Rewrite equation 13,
% 2.32/2.68 lhs with equations [16]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 23: multiply(a(), c()) = multiply(a(), b()).
% 2.32/2.68 Proof: Rewrite equation 17,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [16].
% 2.32/2.68
% 2.32/2.68 24: multiplicative_identity() = inverse(multiply(a(), b())).
% 2.32/2.68 Proof: A critical pair between equations 6 and 22.
% 2.32/2.68
% 2.32/2.68 34: multiply(add(X4, X5), X3) = add(multiply(X3, X4), multiply(X3, X5)).
% 2.32/2.68 Proof: A critical pair between equations 1 and 5.
% 2.32/2.68
% 2.32/2.68 36: multiply(add(X4, X5), X3) = multiply(X3, add(X4, X5)).
% 2.32/2.68 Proof: Rewrite equation 34,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [5].
% 2.32/2.68
% 2.32/2.68 39: multiplicative_identity() = inverse(multiply(a(), c())).
% 2.32/2.68 Proof: Rewrite equation 24,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [23].
% 2.32/2.68
% 2.32/2.68 41: add(a(), c()) = inverse(multiply(a(), c())).
% 2.32/2.68 Proof: Rewrite equation 15,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [39].
% 2.32/2.68
% 2.32/2.68 42: add(a(), b()) = inverse(multiply(a(), c())).
% 2.32/2.68 Proof: Rewrite equation 14,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [39].
% 2.32/2.68
% 2.32/2.68 43: add(multiply(a(), c()), X0) = X0.
% 2.32/2.68 Proof: Rewrite equation 22,
% 2.32/2.68 lhs with equations [23]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 45: multiply(inverse(multiply(a(), c())), X0) = X0.
% 2.32/2.68 Proof: Rewrite equation 11,
% 2.32/2.68 lhs with equations [39]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 57: multiply(add(X6, X7), X3) = multiply(X3, add(X7, X6)).
% 2.32/2.68 Proof: A critical pair between equations 36 and 0.
% 2.32/2.68
% 2.32/2.68 67: add(multiply(a(), X0), multiply(c(), X0)) = X0.
% 2.32/2.68 Proof: Rewrite equation 45,
% 2.32/2.68 lhs with equations [41,4]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 68: add(a(), b()) = add(a(), c()).
% 2.32/2.68 Proof: Rewrite equation 42,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [41].
% 2.32/2.68
% 2.32/2.68 75: add(multiply(X6, X3), multiply(X7, X3)) = add(multiply(X3, X7), multiply(X3, X6)).
% 2.32/2.68 Proof: Rewrite equation 57,
% 2.32/2.68 lhs with equations [4]
% 2.32/2.68 rhs with equations [5].
% 2.32/2.68
% 2.32/2.68 81: c() = multiply(c(), c()).
% 2.32/2.68 Proof: A critical pair between equations 67 and 43.
% 2.32/2.68
% 2.32/2.68 84: b() = add(multiply(a(), c()), multiply(c(), b())).
% 2.32/2.68 Proof: A critical pair between equations 67 and 23.
% 2.32/2.68
% 2.32/2.68 89: add(multiply(c(), X7), multiply(c(), a())) = multiply(X7, c()).
% 2.32/2.68 Proof: A critical pair between equations 75 and 43.
% 2.32/2.68
% 2.32/2.68 93: multiply(c(), add(X7, a())) = multiply(X7, c()).
% 2.32/2.68 Proof: Rewrite equation 89,
% 2.32/2.68 lhs with equations [5]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 97: b() = c().
% 2.32/2.68 Proof: Rewrite equation 84,
% 2.32/2.68 lhs with equations []
% 2.32/2.68 rhs with equations [1,5,68,0,93,81].
% 2.32/2.68
% 2.32/2.68 116: b() = c().
% 2.32/2.68 Proof: Rewrite lhs with equations [97]
% 2.32/2.68 rhs with equations [].
% 2.32/2.68
% 2.32/2.68 % SZS output end Proof
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